Identifier
Mp00017:
Binary trees
—to 312-avoiding permutation⟶
Permutations
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Images
=>
Cc0010;cc-rep-0
[.,.]=>[1]=>[1]=>[1]
[.,[.,.]]=>[2,1]=>[2,1]=>[2,1]
[[.,.],.]=>[1,2]=>[1,2]=>[1,2]
[.,[.,[.,.]]]=>[3,2,1]=>[3,2,1]=>[2,3,1]
[.,[[.,.],.]]=>[2,3,1]=>[3,1,2]=>[3,1,2]
[[.,.],[.,.]]=>[1,3,2]=>[1,3,2]=>[1,3,2]
[[.,[.,.]],.]=>[2,1,3]=>[2,1,3]=>[2,1,3]
[[[.,.],.],.]=>[1,2,3]=>[1,2,3]=>[1,2,3]
[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[4,3,2,1]=>[2,3,4,1]
[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[4,2,1,3]=>[2,4,1,3]
[.,[[.,.],[.,.]]]=>[2,4,3,1]=>[4,3,1,2]=>[3,1,4,2]
[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[4,1,3,2]=>[4,3,1,2]
[.,[[[.,.],.],.]]=>[2,3,4,1]=>[4,1,2,3]=>[4,1,2,3]
[[.,.],[.,[.,.]]]=>[1,4,3,2]=>[1,4,3,2]=>[1,3,4,2]
[[.,.],[[.,.],.]]=>[1,3,4,2]=>[1,4,2,3]=>[1,4,2,3]
[[.,[.,.]],[.,.]]=>[2,1,4,3]=>[2,1,4,3]=>[2,1,4,3]
[[[.,.],.],[.,.]]=>[1,2,4,3]=>[1,2,4,3]=>[1,2,4,3]
[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[3,2,1,4]=>[2,3,1,4]
[[.,[[.,.],.]],.]=>[2,3,1,4]=>[3,1,2,4]=>[3,1,2,4]
[[[.,.],[.,.]],.]=>[1,3,2,4]=>[1,3,2,4]=>[1,3,2,4]
[[[.,[.,.]],.],.]=>[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]
[[[[.,.],.],.],.]=>[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]
[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[2,3,4,5,1]
[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[5,3,2,1,4]=>[2,3,5,1,4]
[.,[.,[[.,.],[.,.]]]]=>[3,5,4,2,1]=>[5,4,2,1,3]=>[2,4,1,5,3]
[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[5,2,1,4,3]=>[2,5,4,1,3]
[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[5,2,1,3,4]=>[2,5,1,3,4]
[.,[[.,.],[.,[.,.]]]]=>[2,5,4,3,1]=>[5,4,3,1,2]=>[3,1,4,5,2]
[.,[[.,.],[[.,.],.]]]=>[2,4,5,3,1]=>[5,3,1,2,4]=>[3,1,5,2,4]
[.,[[.,[.,.]],[.,.]]]=>[3,2,5,4,1]=>[5,4,1,3,2]=>[4,3,1,5,2]
[.,[[[.,.],.],[.,.]]]=>[2,3,5,4,1]=>[5,4,1,2,3]=>[4,1,2,5,3]
[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[5,1,4,3,2]=>[5,3,4,1,2]
[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[5,1,4,2,3]=>[5,4,2,1,3]
[.,[[[.,.],[.,.]],.]]=>[2,4,3,5,1]=>[5,1,2,4,3]=>[5,1,4,2,3]
[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[5,1,3,2,4]=>[5,3,1,2,4]
[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[5,1,2,3,4]
[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]=>[1,5,4,3,2]=>[1,3,4,5,2]
[[.,.],[.,[[.,.],.]]]=>[1,4,5,3,2]=>[1,5,3,2,4]=>[1,3,5,2,4]
[[.,.],[[.,.],[.,.]]]=>[1,3,5,4,2]=>[1,5,4,2,3]=>[1,4,2,5,3]
[[.,.],[[.,[.,.]],.]]=>[1,4,3,5,2]=>[1,5,2,4,3]=>[1,5,4,2,3]
[[.,.],[[[.,.],.],.]]=>[1,3,4,5,2]=>[1,5,2,3,4]=>[1,5,2,3,4]
[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]=>[2,1,5,4,3]=>[2,1,4,5,3]
[[.,[.,.]],[[.,.],.]]=>[2,1,4,5,3]=>[2,1,5,3,4]=>[2,1,5,3,4]
[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]=>[1,2,5,4,3]=>[1,2,4,5,3]
[[[.,.],.],[[.,.],.]]=>[1,2,4,5,3]=>[1,2,5,3,4]=>[1,2,5,3,4]
[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]=>[3,2,1,5,4]=>[2,3,1,5,4]
[[.,[[.,.],.]],[.,.]]=>[2,3,1,5,4]=>[3,1,2,5,4]=>[3,1,2,5,4]
[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[1,3,2,5,4]
[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[2,1,3,5,4]
[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[1,2,3,5,4]
[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[2,3,4,1,5]
[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[4,2,1,3,5]=>[2,4,1,3,5]
[[.,[[.,.],[.,.]]],.]=>[2,4,3,1,5]=>[4,3,1,2,5]=>[3,1,4,2,5]
[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[4,1,3,2,5]=>[4,3,1,2,5]
[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[4,1,2,3,5]
[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]=>[1,4,3,2,5]=>[1,3,4,2,5]
[[[.,.],[[.,.],.]],.]=>[1,3,4,2,5]=>[1,4,2,3,5]=>[1,4,2,3,5]
[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[2,1,4,3,5]
[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[1,2,4,3,5]
[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[2,3,1,4,5]
[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[3,1,2,4,5]
[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[1,3,2,4,5]
[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,3,4,5]
[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]
[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]
[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]
[.,[.,[.,[[.,.],[.,.]]]]]=>[4,6,5,3,2,1]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]
[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[6,3,2,1,5,4]=>[2,3,6,5,1,4]
[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]
[.,[.,[[.,.],[.,[.,.]]]]]=>[3,6,5,4,2,1]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]
[.,[.,[[.,.],[[.,.],.]]]]=>[3,5,6,4,2,1]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]
[.,[.,[[.,[.,.]],[.,.]]]]=>[4,3,6,5,2,1]=>[6,5,2,1,4,3]=>[2,5,4,1,6,3]
[.,[.,[[[.,.],.],[.,.]]]]=>[3,4,6,5,2,1]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]
[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[6,2,1,5,4,3]=>[2,6,4,5,1,3]
[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[6,2,1,5,3,4]=>[2,6,5,3,1,4]
[.,[.,[[[.,.],[.,.]],.]]]=>[3,5,4,6,2,1]=>[6,2,1,3,5,4]=>[2,6,1,5,3,4]
[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[6,2,1,4,3,5]=>[2,6,4,1,3,5]
[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]
[.,[[.,.],[.,[.,[.,.]]]]]=>[2,6,5,4,3,1]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]
[.,[[.,.],[.,[[.,.],.]]]]=>[2,5,6,4,3,1]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]
[.,[[.,.],[[.,.],[.,.]]]]=>[2,4,6,5,3,1]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]
[.,[[.,.],[[.,[.,.]],.]]]=>[2,5,4,6,3,1]=>[6,3,1,2,5,4]=>[3,1,6,5,2,4]
[.,[[.,.],[[[.,.],.],.]]]=>[2,4,5,6,3,1]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]
[.,[[.,[.,.]],[.,[.,.]]]]=>[3,2,6,5,4,1]=>[6,5,4,1,3,2]=>[4,3,1,5,6,2]
[.,[[.,[.,.]],[[.,.],.]]]=>[3,2,5,6,4,1]=>[6,4,1,3,2,5]=>[4,3,1,6,2,5]
[.,[[[.,.],.],[.,[.,.]]]]=>[2,3,6,5,4,1]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]
[.,[[[.,.],.],[[.,.],.]]]=>[2,3,5,6,4,1]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]
[.,[[.,[.,[.,.]]],[.,.]]]=>[4,3,2,6,5,1]=>[6,5,1,4,3,2]=>[5,3,4,1,6,2]
[.,[[.,[[.,.],.]],[.,.]]]=>[3,4,2,6,5,1]=>[6,5,1,4,2,3]=>[5,4,2,1,6,3]
[.,[[[.,.],[.,.]],[.,.]]]=>[2,4,3,6,5,1]=>[6,5,1,2,4,3]=>[5,1,4,2,6,3]
[.,[[[.,[.,.]],.],[.,.]]]=>[3,2,4,6,5,1]=>[6,5,1,3,2,4]=>[5,3,1,2,6,4]
[.,[[[[.,.],.],.],[.,.]]]=>[2,3,4,6,5,1]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]
[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[6,1,5,4,3,2]=>[6,3,4,5,1,2]
[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[6,1,5,3,2,4]=>[6,3,5,2,1,4]
[.,[[.,[[.,.],[.,.]]],.]]=>[3,5,4,2,6,1]=>[6,1,5,4,2,3]=>[6,4,2,5,1,3]
[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[6,1,5,2,4,3]=>[6,5,4,2,1,3]
[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[6,1,5,2,3,4]=>[6,5,2,3,1,4]
[.,[[[.,.],[.,[.,.]]],.]]=>[2,5,4,3,6,1]=>[6,1,2,5,4,3]=>[6,1,4,5,2,3]
[.,[[[.,.],[[.,.],.]],.]]=>[2,4,5,3,6,1]=>[6,1,2,5,3,4]=>[6,1,5,3,2,4]
[.,[[[.,[.,.]],[.,.]],.]]=>[3,2,5,4,6,1]=>[6,1,3,2,5,4]=>[6,3,1,5,2,4]
[.,[[[[.,.],.],[.,.]],.]]=>[2,3,5,4,6,1]=>[6,1,2,3,5,4]=>[6,1,2,5,3,4]
[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[6,1,4,3,2,5]=>[6,3,4,1,2,5]
[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[6,1,4,2,3,5]=>[6,4,2,1,3,5]
[.,[[[[.,.],[.,.]],.],.]]=>[2,4,3,5,6,1]=>[6,1,2,4,3,5]=>[6,1,4,2,3,5]
[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[6,1,3,2,4,5]=>[6,3,1,2,4,5]
[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]
[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]=>[1,6,5,4,3,2]=>[1,3,4,5,6,2]
[[.,.],[.,[.,[[.,.],.]]]]=>[1,5,6,4,3,2]=>[1,6,4,3,2,5]=>[1,3,4,6,2,5]
[[.,.],[.,[[.,.],[.,.]]]]=>[1,4,6,5,3,2]=>[1,6,5,3,2,4]=>[1,3,5,2,6,4]
[[.,.],[.,[[.,[.,.]],.]]]=>[1,5,4,6,3,2]=>[1,6,3,2,5,4]=>[1,3,6,5,2,4]
[[.,.],[.,[[[.,.],.],.]]]=>[1,4,5,6,3,2]=>[1,6,3,2,4,5]=>[1,3,6,2,4,5]
[[.,.],[[.,.],[.,[.,.]]]]=>[1,3,6,5,4,2]=>[1,6,5,4,2,3]=>[1,4,2,5,6,3]
[[.,.],[[.,.],[[.,.],.]]]=>[1,3,5,6,4,2]=>[1,6,4,2,3,5]=>[1,4,2,6,3,5]
[[.,.],[[.,[.,.]],[.,.]]]=>[1,4,3,6,5,2]=>[1,6,5,2,4,3]=>[1,5,4,2,6,3]
[[.,.],[[[.,.],.],[.,.]]]=>[1,3,4,6,5,2]=>[1,6,5,2,3,4]=>[1,5,2,3,6,4]
[[.,.],[[.,[.,[.,.]]],.]]=>[1,5,4,3,6,2]=>[1,6,2,5,4,3]=>[1,6,4,5,2,3]
[[.,.],[[.,[[.,.],.]],.]]=>[1,4,5,3,6,2]=>[1,6,2,5,3,4]=>[1,6,5,3,2,4]
[[.,.],[[[.,.],[.,.]],.]]=>[1,3,5,4,6,2]=>[1,6,2,3,5,4]=>[1,6,2,5,3,4]
[[.,.],[[[.,[.,.]],.],.]]=>[1,4,3,5,6,2]=>[1,6,2,4,3,5]=>[1,6,4,2,3,5]
[[.,.],[[[[.,.],.],.],.]]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>[1,6,2,3,4,5]
[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]=>[2,1,6,5,4,3]=>[2,1,4,5,6,3]
[[.,[.,.]],[.,[[.,.],.]]]=>[2,1,5,6,4,3]=>[2,1,6,4,3,5]=>[2,1,4,6,3,5]
[[.,[.,.]],[[.,.],[.,.]]]=>[2,1,4,6,5,3]=>[2,1,6,5,3,4]=>[2,1,5,3,6,4]
[[.,[.,.]],[[.,[.,.]],.]]=>[2,1,5,4,6,3]=>[2,1,6,3,5,4]=>[2,1,6,5,3,4]
[[.,[.,.]],[[[.,.],.],.]]=>[2,1,4,5,6,3]=>[2,1,6,3,4,5]=>[2,1,6,3,4,5]
[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]=>[1,2,6,5,4,3]=>[1,2,4,5,6,3]
[[[.,.],.],[.,[[.,.],.]]]=>[1,2,5,6,4,3]=>[1,2,6,4,3,5]=>[1,2,4,6,3,5]
[[[.,.],.],[[.,.],[.,.]]]=>[1,2,4,6,5,3]=>[1,2,6,5,3,4]=>[1,2,5,3,6,4]
[[[.,.],.],[[.,[.,.]],.]]=>[1,2,5,4,6,3]=>[1,2,6,3,5,4]=>[1,2,6,5,3,4]
[[[.,.],.],[[[.,.],.],.]]=>[1,2,4,5,6,3]=>[1,2,6,3,4,5]=>[1,2,6,3,4,5]
[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]
[[.,[.,[.,.]]],[[.,.],.]]=>[3,2,1,5,6,4]=>[3,2,1,6,4,5]=>[2,3,1,6,4,5]
[[.,[[.,.],.]],[.,[.,.]]]=>[2,3,1,6,5,4]=>[3,1,2,6,5,4]=>[3,1,2,5,6,4]
[[.,[[.,.],.]],[[.,.],.]]=>[2,3,1,5,6,4]=>[3,1,2,6,4,5]=>[3,1,2,6,4,5]
[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]
[[[.,.],[.,.]],[[.,.],.]]=>[1,3,2,5,6,4]=>[1,3,2,6,4,5]=>[1,3,2,6,4,5]
[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]
[[[.,[.,.]],.],[[.,.],.]]=>[2,1,3,5,6,4]=>[2,1,3,6,4,5]=>[2,1,3,6,4,5]
[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]
[[[[.,.],.],.],[[.,.],.]]=>[1,2,3,5,6,4]=>[1,2,3,6,4,5]=>[1,2,3,6,4,5]
[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>[2,3,4,1,6,5]
[[.,[.,[[.,.],.]]],[.,.]]=>[3,4,2,1,6,5]=>[4,2,1,3,6,5]=>[2,4,1,3,6,5]
[[.,[[.,.],[.,.]]],[.,.]]=>[2,4,3,1,6,5]=>[4,3,1,2,6,5]=>[3,1,4,2,6,5]
[[.,[[.,[.,.]],.]],[.,.]]=>[3,2,4,1,6,5]=>[4,1,3,2,6,5]=>[4,3,1,2,6,5]
[[.,[[[.,.],.],.]],[.,.]]=>[2,3,4,1,6,5]=>[4,1,2,3,6,5]=>[4,1,2,3,6,5]
[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]
[[[.,.],[[.,.],.]],[.,.]]=>[1,3,4,2,6,5]=>[1,4,2,3,6,5]=>[1,4,2,3,6,5]
[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]
[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]
[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]
[[[.,[[.,.],.]],.],[.,.]]=>[2,3,1,4,6,5]=>[3,1,2,4,6,5]=>[3,1,2,4,6,5]
[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]
[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]
[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]
[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]
[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[5,3,2,1,4,6]=>[2,3,5,1,4,6]
[[.,[.,[[.,.],[.,.]]]],.]=>[3,5,4,2,1,6]=>[5,4,2,1,3,6]=>[2,4,1,5,3,6]
[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[5,2,1,4,3,6]=>[2,5,4,1,3,6]
[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]
[[.,[[.,.],[.,[.,.]]]],.]=>[2,5,4,3,1,6]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]
[[.,[[.,.],[[.,.],.]]],.]=>[2,4,5,3,1,6]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]
[[.,[[.,[.,.]],[.,.]]],.]=>[3,2,5,4,1,6]=>[5,4,1,3,2,6]=>[4,3,1,5,2,6]
[[.,[[[.,.],.],[.,.]]],.]=>[2,3,5,4,1,6]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]
[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[5,1,4,3,2,6]=>[5,3,4,1,2,6]
[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[5,1,4,2,3,6]=>[5,4,2,1,3,6]
[[.,[[[.,.],[.,.]],.]],.]=>[2,4,3,5,1,6]=>[5,1,2,4,3,6]=>[5,1,4,2,3,6]
[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[5,1,3,2,4,6]=>[5,3,1,2,4,6]
[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]
[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]=>[1,5,4,3,2,6]=>[1,3,4,5,2,6]
[[[.,.],[.,[[.,.],.]]],.]=>[1,4,5,3,2,6]=>[1,5,3,2,4,6]=>[1,3,5,2,4,6]
[[[.,.],[[.,.],[.,.]]],.]=>[1,3,5,4,2,6]=>[1,5,4,2,3,6]=>[1,4,2,5,3,6]
[[[.,.],[[.,[.,.]],.]],.]=>[1,4,3,5,2,6]=>[1,5,2,4,3,6]=>[1,5,4,2,3,6]
[[[.,.],[[[.,.],.],.]],.]=>[1,3,4,5,2,6]=>[1,5,2,3,4,6]=>[1,5,2,3,4,6]
[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]
[[[.,[.,.]],[[.,.],.]],.]=>[2,1,4,5,3,6]=>[2,1,5,3,4,6]=>[2,1,5,3,4,6]
[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]
[[[[.,.],.],[[.,.],.]],.]=>[1,2,4,5,3,6]=>[1,2,5,3,4,6]=>[1,2,5,3,4,6]
[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]=>[3,2,1,5,4,6]=>[2,3,1,5,4,6]
[[[.,[[.,.],.]],[.,.]],.]=>[2,3,1,5,4,6]=>[3,1,2,5,4,6]=>[3,1,2,5,4,6]
[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]
[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]
[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]
[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]
[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]
[[[.,[[.,.],[.,.]]],.],.]=>[2,4,3,1,5,6]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]
[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[4,1,3,2,5,6]=>[4,3,1,2,5,6]
[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]
[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]
[[[[.,.],[[.,.],.]],.],.]=>[1,3,4,2,5,6]=>[1,4,2,3,5,6]=>[1,4,2,3,5,6]
[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]
[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]
[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]
[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]
[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]
[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]
[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]
[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]
[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[5,7,6,4,3,2,1]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]
[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[7,4,3,2,1,6,5]=>[2,3,4,7,6,1,5]
[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]
[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[4,7,6,5,3,2,1]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]
[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[4,6,7,5,3,2,1]=>[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]
[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[5,4,7,6,3,2,1]=>[7,6,3,2,1,5,4]=>[2,3,6,5,1,7,4]
[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[4,5,7,6,3,2,1]=>[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]
[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[7,3,2,1,6,5,4]=>[2,3,7,5,6,1,4]
[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[7,3,2,1,6,4,5]=>[2,3,7,6,4,1,5]
[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[4,6,5,7,3,2,1]=>[7,3,2,1,4,6,5]=>[2,3,7,1,6,4,5]
[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[7,3,2,1,5,4,6]=>[2,3,7,5,1,4,6]
[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]
[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[3,7,6,5,4,2,1]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]
[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[3,6,7,5,4,2,1]=>[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]
[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[3,5,7,6,4,2,1]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]
[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[3,6,5,7,4,2,1]=>[7,4,2,1,3,6,5]=>[2,4,1,7,6,3,5]
[.,[.,[[.,.],[[[.,.],.],.]]]]=>[3,5,6,7,4,2,1]=>[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]
[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[4,3,7,6,5,2,1]=>[7,6,5,2,1,4,3]=>[2,5,4,1,6,7,3]
[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[4,3,6,7,5,2,1]=>[7,5,2,1,4,3,6]=>[2,5,4,1,7,3,6]
[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[3,4,7,6,5,2,1]=>[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]
[.,[.,[[[.,.],.],[[.,.],.]]]]=>[3,4,6,7,5,2,1]=>[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]
[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[5,4,3,7,6,2,1]=>[7,6,2,1,5,4,3]=>[2,6,4,5,1,7,3]
[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[4,5,3,7,6,2,1]=>[7,6,2,1,5,3,4]=>[2,6,5,3,1,7,4]
[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[3,5,4,7,6,2,1]=>[7,6,2,1,3,5,4]=>[2,6,1,5,3,7,4]
[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[4,3,5,7,6,2,1]=>[7,6,2,1,4,3,5]=>[2,6,4,1,3,7,5]
[.,[.,[[[[.,.],.],.],[.,.]]]]=>[3,4,5,7,6,2,1]=>[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]
[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[7,2,1,6,5,4,3]=>[2,7,4,5,6,1,3]
[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[7,2,1,6,4,3,5]=>[2,7,4,6,3,1,5]
[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[4,6,5,3,7,2,1]=>[7,2,1,6,5,3,4]=>[2,7,5,3,6,1,4]
[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[7,2,1,6,3,5,4]=>[2,7,6,5,3,1,4]
[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[7,2,1,6,3,4,5]=>[2,7,6,3,4,1,5]
[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[3,6,5,4,7,2,1]=>[7,2,1,3,6,5,4]=>[2,7,1,5,6,3,4]
[.,[.,[[[.,.],[[.,.],.]],.]]]=>[3,5,6,4,7,2,1]=>[7,2,1,3,6,4,5]=>[2,7,1,6,4,3,5]
[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[4,3,6,5,7,2,1]=>[7,2,1,4,3,6,5]=>[2,7,4,1,6,3,5]
[.,[.,[[[[.,.],.],[.,.]],.]]]=>[3,4,6,5,7,2,1]=>[7,2,1,3,4,6,5]=>[2,7,1,3,6,4,5]
[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[7,2,1,5,4,3,6]=>[2,7,4,5,1,3,6]
[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[7,2,1,5,3,4,6]=>[2,7,5,3,1,4,6]
[.,[.,[[[[.,.],[.,.]],.],.]]]=>[3,5,4,6,7,2,1]=>[7,2,1,3,5,4,6]=>[2,7,1,5,3,4,6]
[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[7,2,1,4,3,5,6]=>[2,7,4,1,3,5,6]
[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]
[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[2,7,6,5,4,3,1]=>[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]
[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[2,6,7,5,4,3,1]=>[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]
[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[2,5,7,6,4,3,1]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]
[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[2,6,5,7,4,3,1]=>[7,4,3,1,2,6,5]=>[3,1,4,7,6,2,5]
[.,[[.,.],[.,[[[.,.],.],.]]]]=>[2,5,6,7,4,3,1]=>[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]
[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[2,4,7,6,5,3,1]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]
[.,[[.,.],[[.,.],[[.,.],.]]]]=>[2,4,6,7,5,3,1]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]
[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[2,5,4,7,6,3,1]=>[7,6,3,1,2,5,4]=>[3,1,6,5,2,7,4]
[.,[[.,.],[[[.,.],.],[.,.]]]]=>[2,4,5,7,6,3,1]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]
[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[2,6,5,4,7,3,1]=>[7,3,1,2,6,5,4]=>[3,1,7,5,6,2,4]
[.,[[.,.],[[.,[[.,.],.]],.]]]=>[2,5,6,4,7,3,1]=>[7,3,1,2,6,4,5]=>[3,1,7,6,4,2,5]
[.,[[.,.],[[[.,.],[.,.]],.]]]=>[2,4,6,5,7,3,1]=>[7,3,1,2,4,6,5]=>[3,1,7,2,6,4,5]
[.,[[.,.],[[[.,[.,.]],.],.]]]=>[2,5,4,6,7,3,1]=>[7,3,1,2,5,4,6]=>[3,1,7,5,2,4,6]
[.,[[.,.],[[[[.,.],.],.],.]]]=>[2,4,5,6,7,3,1]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]
[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[3,2,7,6,5,4,1]=>[7,6,5,4,1,3,2]=>[4,3,1,5,6,7,2]
[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[3,2,6,7,5,4,1]=>[7,5,4,1,3,2,6]=>[4,3,1,5,7,2,6]
[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[3,2,5,7,6,4,1]=>[7,6,4,1,3,2,5]=>[4,3,1,6,2,7,5]
[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[3,2,6,5,7,4,1]=>[7,4,1,3,2,6,5]=>[4,3,1,7,6,2,5]
[.,[[.,[.,.]],[[[.,.],.],.]]]=>[3,2,5,6,7,4,1]=>[7,4,1,3,2,5,6]=>[4,3,1,7,2,5,6]
[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[2,3,7,6,5,4,1]=>[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]
[.,[[[.,.],.],[.,[[.,.],.]]]]=>[2,3,6,7,5,4,1]=>[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]
[.,[[[.,.],.],[[.,.],[.,.]]]]=>[2,3,5,7,6,4,1]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]
[.,[[[.,.],.],[[.,[.,.]],.]]]=>[2,3,6,5,7,4,1]=>[7,4,1,2,3,6,5]=>[4,1,2,7,6,3,5]
[.,[[[.,.],.],[[[.,.],.],.]]]=>[2,3,5,6,7,4,1]=>[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]
[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[4,3,2,7,6,5,1]=>[7,6,5,1,4,3,2]=>[5,3,4,1,6,7,2]
[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[4,3,2,6,7,5,1]=>[7,5,1,4,3,2,6]=>[5,3,4,1,7,2,6]
[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[3,4,2,7,6,5,1]=>[7,6,5,1,4,2,3]=>[5,4,2,1,6,7,3]
[.,[[.,[[.,.],.]],[[.,.],.]]]=>[3,4,2,6,7,5,1]=>[7,5,1,4,2,3,6]=>[5,4,2,1,7,3,6]
[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[2,4,3,7,6,5,1]=>[7,6,5,1,2,4,3]=>[5,1,4,2,6,7,3]
[.,[[[.,.],[.,.]],[[.,.],.]]]=>[2,4,3,6,7,5,1]=>[7,5,1,2,4,3,6]=>[5,1,4,2,7,3,6]
[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[3,2,4,7,6,5,1]=>[7,6,5,1,3,2,4]=>[5,3,1,2,6,7,4]
[.,[[[.,[.,.]],.],[[.,.],.]]]=>[3,2,4,6,7,5,1]=>[7,5,1,3,2,4,6]=>[5,3,1,2,7,4,6]
[.,[[[[.,.],.],.],[.,[.,.]]]]=>[2,3,4,7,6,5,1]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]
[.,[[[[.,.],.],.],[[.,.],.]]]=>[2,3,4,6,7,5,1]=>[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]
[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[5,4,3,2,7,6,1]=>[7,6,1,5,4,3,2]=>[6,3,4,5,1,7,2]
[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[4,5,3,2,7,6,1]=>[7,6,1,5,3,2,4]=>[6,3,5,2,1,7,4]
[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[3,5,4,2,7,6,1]=>[7,6,1,5,4,2,3]=>[6,4,2,5,1,7,3]
[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[4,3,5,2,7,6,1]=>[7,6,1,5,2,4,3]=>[6,5,4,2,1,7,3]
[.,[[.,[[[.,.],.],.]],[.,.]]]=>[3,4,5,2,7,6,1]=>[7,6,1,5,2,3,4]=>[6,5,2,3,1,7,4]
[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[2,5,4,3,7,6,1]=>[7,6,1,2,5,4,3]=>[6,1,4,5,2,7,3]
[.,[[[.,.],[[.,.],.]],[.,.]]]=>[2,4,5,3,7,6,1]=>[7,6,1,2,5,3,4]=>[6,1,5,3,2,7,4]
[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[3,2,5,4,7,6,1]=>[7,6,1,3,2,5,4]=>[6,3,1,5,2,7,4]
[.,[[[[.,.],.],[.,.]],[.,.]]]=>[2,3,5,4,7,6,1]=>[7,6,1,2,3,5,4]=>[6,1,2,5,3,7,4]
[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[4,3,2,5,7,6,1]=>[7,6,1,4,3,2,5]=>[6,3,4,1,2,7,5]
[.,[[[.,[[.,.],.]],.],[.,.]]]=>[3,4,2,5,7,6,1]=>[7,6,1,4,2,3,5]=>[6,4,2,1,3,7,5]
[.,[[[[.,.],[.,.]],.],[.,.]]]=>[2,4,3,5,7,6,1]=>[7,6,1,2,4,3,5]=>[6,1,4,2,3,7,5]
[.,[[[[.,[.,.]],.],.],[.,.]]]=>[3,2,4,5,7,6,1]=>[7,6,1,3,2,4,5]=>[6,3,1,2,4,7,5]
[.,[[[[[.,.],.],.],.],[.,.]]]=>[2,3,4,5,7,6,1]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]
[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[7,1,6,5,4,3,2]=>[7,3,4,5,6,1,2]
[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[7,1,6,4,3,2,5]=>[7,3,4,6,2,1,5]
[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[4,6,5,3,2,7,1]=>[7,1,6,5,3,2,4]=>[7,3,5,2,6,1,4]
[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[7,1,6,3,2,5,4]=>[7,3,6,5,2,1,4]
[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[7,1,6,3,2,4,5]=>[7,3,6,2,4,1,5]
[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[3,6,5,4,2,7,1]=>[7,1,6,5,4,2,3]=>[7,4,2,5,6,1,3]
[.,[[.,[[.,.],[[.,.],.]]],.]]=>[3,5,6,4,2,7,1]=>[7,1,6,4,2,3,5]=>[7,4,2,6,3,1,5]
[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[4,3,6,5,2,7,1]=>[7,1,6,5,2,4,3]=>[7,5,4,2,6,1,3]
[.,[[.,[[[.,.],.],[.,.]]],.]]=>[3,4,6,5,2,7,1]=>[7,1,6,5,2,3,4]=>[7,5,2,3,6,1,4]
[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[7,1,6,2,5,4,3]=>[7,6,4,5,2,1,3]
[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[7,1,6,2,5,3,4]=>[7,6,5,3,2,1,4]
[.,[[.,[[[.,.],[.,.]],.]],.]]=>[3,5,4,6,2,7,1]=>[7,1,6,2,3,5,4]=>[7,6,2,5,3,1,4]
[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[7,1,6,2,4,3,5]=>[7,6,4,2,3,1,5]
[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[7,1,6,2,3,4,5]=>[7,6,2,3,4,1,5]
[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[2,6,5,4,3,7,1]=>[7,1,2,6,5,4,3]=>[7,1,4,5,6,2,3]
[.,[[[.,.],[.,[[.,.],.]]],.]]=>[2,5,6,4,3,7,1]=>[7,1,2,6,4,3,5]=>[7,1,4,6,3,2,5]
[.,[[[.,.],[[.,.],[.,.]]],.]]=>[2,4,6,5,3,7,1]=>[7,1,2,6,5,3,4]=>[7,1,5,3,6,2,4]
[.,[[[.,.],[[.,[.,.]],.]],.]]=>[2,5,4,6,3,7,1]=>[7,1,2,6,3,5,4]=>[7,1,6,5,3,2,4]
[.,[[[.,.],[[[.,.],.],.]],.]]=>[2,4,5,6,3,7,1]=>[7,1,2,6,3,4,5]=>[7,1,6,3,4,2,5]
[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[3,2,6,5,4,7,1]=>[7,1,3,2,6,5,4]=>[7,3,1,5,6,2,4]
[.,[[[.,[.,.]],[[.,.],.]],.]]=>[3,2,5,6,4,7,1]=>[7,1,3,2,6,4,5]=>[7,3,1,6,4,2,5]
[.,[[[[.,.],.],[.,[.,.]]],.]]=>[2,3,6,5,4,7,1]=>[7,1,2,3,6,5,4]=>[7,1,2,5,6,3,4]
[.,[[[[.,.],.],[[.,.],.]],.]]=>[2,3,5,6,4,7,1]=>[7,1,2,3,6,4,5]=>[7,1,2,6,4,3,5]
[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[4,3,2,6,5,7,1]=>[7,1,4,3,2,6,5]=>[7,3,4,1,6,2,5]
[.,[[[.,[[.,.],.]],[.,.]],.]]=>[3,4,2,6,5,7,1]=>[7,1,4,2,3,6,5]=>[7,4,2,1,6,3,5]
[.,[[[[.,.],[.,.]],[.,.]],.]]=>[2,4,3,6,5,7,1]=>[7,1,2,4,3,6,5]=>[7,1,4,2,6,3,5]
[.,[[[[.,[.,.]],.],[.,.]],.]]=>[3,2,4,6,5,7,1]=>[7,1,3,2,4,6,5]=>[7,3,1,2,6,4,5]
[.,[[[[[.,.],.],.],[.,.]],.]]=>[2,3,4,6,5,7,1]=>[7,1,2,3,4,6,5]=>[7,1,2,3,6,4,5]
[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[7,1,5,4,3,2,6]=>[7,3,4,5,1,2,6]
[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[7,1,5,3,2,4,6]=>[7,3,5,2,1,4,6]
[.,[[[.,[[.,.],[.,.]]],.],.]]=>[3,5,4,2,6,7,1]=>[7,1,5,4,2,3,6]=>[7,4,2,5,1,3,6]
[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[7,1,5,2,4,3,6]=>[7,5,4,2,1,3,6]
[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[7,1,5,2,3,4,6]=>[7,5,2,3,1,4,6]
[.,[[[[.,.],[.,[.,.]]],.],.]]=>[2,5,4,3,6,7,1]=>[7,1,2,5,4,3,6]=>[7,1,4,5,2,3,6]
[.,[[[[.,.],[[.,.],.]],.],.]]=>[2,4,5,3,6,7,1]=>[7,1,2,5,3,4,6]=>[7,1,5,3,2,4,6]
[.,[[[[.,[.,.]],[.,.]],.],.]]=>[3,2,5,4,6,7,1]=>[7,1,3,2,5,4,6]=>[7,3,1,5,2,4,6]
[.,[[[[[.,.],.],[.,.]],.],.]]=>[2,3,5,4,6,7,1]=>[7,1,2,3,5,4,6]=>[7,1,2,5,3,4,6]
[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[7,1,4,3,2,5,6]=>[7,3,4,1,2,5,6]
[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[7,1,4,2,3,5,6]=>[7,4,2,1,3,5,6]
[.,[[[[[.,.],[.,.]],.],.],.]]=>[2,4,3,5,6,7,1]=>[7,1,2,4,3,5,6]=>[7,1,4,2,3,5,6]
[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[7,1,3,2,4,5,6]=>[7,3,1,2,4,5,6]
[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]
[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[1,3,4,5,6,7,2]
[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[1,6,7,5,4,3,2]=>[1,7,5,4,3,2,6]=>[1,3,4,5,7,2,6]
[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[1,5,7,6,4,3,2]=>[1,7,6,4,3,2,5]=>[1,3,4,6,2,7,5]
[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[1,6,5,7,4,3,2]=>[1,7,4,3,2,6,5]=>[1,3,4,7,6,2,5]
[[.,.],[.,[.,[[[.,.],.],.]]]]=>[1,5,6,7,4,3,2]=>[1,7,4,3,2,5,6]=>[1,3,4,7,2,5,6]
[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[1,4,7,6,5,3,2]=>[1,7,6,5,3,2,4]=>[1,3,5,2,6,7,4]
[[.,.],[.,[[.,.],[[.,.],.]]]]=>[1,4,6,7,5,3,2]=>[1,7,5,3,2,4,6]=>[1,3,5,2,7,4,6]
[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[1,5,4,7,6,3,2]=>[1,7,6,3,2,5,4]=>[1,3,6,5,2,7,4]
[[.,.],[.,[[[.,.],.],[.,.]]]]=>[1,4,5,7,6,3,2]=>[1,7,6,3,2,4,5]=>[1,3,6,2,4,7,5]
[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[1,6,5,4,7,3,2]=>[1,7,3,2,6,5,4]=>[1,3,7,5,6,2,4]
[[.,.],[.,[[.,[[.,.],.]],.]]]=>[1,5,6,4,7,3,2]=>[1,7,3,2,6,4,5]=>[1,3,7,6,4,2,5]
[[.,.],[.,[[[.,.],[.,.]],.]]]=>[1,4,6,5,7,3,2]=>[1,7,3,2,4,6,5]=>[1,3,7,2,6,4,5]
[[.,.],[.,[[[.,[.,.]],.],.]]]=>[1,5,4,6,7,3,2]=>[1,7,3,2,5,4,6]=>[1,3,7,5,2,4,6]
[[.,.],[.,[[[[.,.],.],.],.]]]=>[1,4,5,6,7,3,2]=>[1,7,3,2,4,5,6]=>[1,3,7,2,4,5,6]
[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[1,3,7,6,5,4,2]=>[1,7,6,5,4,2,3]=>[1,4,2,5,6,7,3]
[[.,.],[[.,.],[.,[[.,.],.]]]]=>[1,3,6,7,5,4,2]=>[1,7,5,4,2,3,6]=>[1,4,2,5,7,3,6]
[[.,.],[[.,.],[[.,.],[.,.]]]]=>[1,3,5,7,6,4,2]=>[1,7,6,4,2,3,5]=>[1,4,2,6,3,7,5]
[[.,.],[[.,.],[[.,[.,.]],.]]]=>[1,3,6,5,7,4,2]=>[1,7,4,2,3,6,5]=>[1,4,2,7,6,3,5]
[[.,.],[[.,.],[[[.,.],.],.]]]=>[1,3,5,6,7,4,2]=>[1,7,4,2,3,5,6]=>[1,4,2,7,3,5,6]
[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[1,4,3,7,6,5,2]=>[1,7,6,5,2,4,3]=>[1,5,4,2,6,7,3]
[[.,.],[[.,[.,.]],[[.,.],.]]]=>[1,4,3,6,7,5,2]=>[1,7,5,2,4,3,6]=>[1,5,4,2,7,3,6]
[[.,.],[[[.,.],.],[.,[.,.]]]]=>[1,3,4,7,6,5,2]=>[1,7,6,5,2,3,4]=>[1,5,2,3,6,7,4]
[[.,.],[[[.,.],.],[[.,.],.]]]=>[1,3,4,6,7,5,2]=>[1,7,5,2,3,4,6]=>[1,5,2,3,7,4,6]
[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[1,5,4,3,7,6,2]=>[1,7,6,2,5,4,3]=>[1,6,4,5,2,7,3]
[[.,.],[[.,[[.,.],.]],[.,.]]]=>[1,4,5,3,7,6,2]=>[1,7,6,2,5,3,4]=>[1,6,5,3,2,7,4]
[[.,.],[[[.,.],[.,.]],[.,.]]]=>[1,3,5,4,7,6,2]=>[1,7,6,2,3,5,4]=>[1,6,2,5,3,7,4]
[[.,.],[[[.,[.,.]],.],[.,.]]]=>[1,4,3,5,7,6,2]=>[1,7,6,2,4,3,5]=>[1,6,4,2,3,7,5]
[[.,.],[[[[.,.],.],.],[.,.]]]=>[1,3,4,5,7,6,2]=>[1,7,6,2,3,4,5]=>[1,6,2,3,4,7,5]
[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[1,6,5,4,3,7,2]=>[1,7,2,6,5,4,3]=>[1,7,4,5,6,2,3]
[[.,.],[[.,[.,[[.,.],.]]],.]]=>[1,5,6,4,3,7,2]=>[1,7,2,6,4,3,5]=>[1,7,4,6,3,2,5]
[[.,.],[[.,[[.,.],[.,.]]],.]]=>[1,4,6,5,3,7,2]=>[1,7,2,6,5,3,4]=>[1,7,5,3,6,2,4]
[[.,.],[[.,[[.,[.,.]],.]],.]]=>[1,5,4,6,3,7,2]=>[1,7,2,6,3,5,4]=>[1,7,6,5,3,2,4]
[[.,.],[[.,[[[.,.],.],.]],.]]=>[1,4,5,6,3,7,2]=>[1,7,2,6,3,4,5]=>[1,7,6,3,4,2,5]
[[.,.],[[[.,.],[.,[.,.]]],.]]=>[1,3,6,5,4,7,2]=>[1,7,2,3,6,5,4]=>[1,7,2,5,6,3,4]
[[.,.],[[[.,.],[[.,.],.]],.]]=>[1,3,5,6,4,7,2]=>[1,7,2,3,6,4,5]=>[1,7,2,6,4,3,5]
[[.,.],[[[.,[.,.]],[.,.]],.]]=>[1,4,3,6,5,7,2]=>[1,7,2,4,3,6,5]=>[1,7,4,2,6,3,5]
[[.,.],[[[[.,.],.],[.,.]],.]]=>[1,3,4,6,5,7,2]=>[1,7,2,3,4,6,5]=>[1,7,2,3,6,4,5]
[[.,.],[[[.,[.,[.,.]]],.],.]]=>[1,5,4,3,6,7,2]=>[1,7,2,5,4,3,6]=>[1,7,4,5,2,3,6]
[[.,.],[[[.,[[.,.],.]],.],.]]=>[1,4,5,3,6,7,2]=>[1,7,2,5,3,4,6]=>[1,7,5,3,2,4,6]
[[.,.],[[[[.,.],[.,.]],.],.]]=>[1,3,5,4,6,7,2]=>[1,7,2,3,5,4,6]=>[1,7,2,5,3,4,6]
[[.,.],[[[[.,[.,.]],.],.],.]]=>[1,4,3,5,6,7,2]=>[1,7,2,4,3,5,6]=>[1,7,4,2,3,5,6]
[[.,.],[[[[[.,.],.],.],.],.]]=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6]
[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[2,1,4,5,6,7,3]
[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[2,1,6,7,5,4,3]=>[2,1,7,5,4,3,6]=>[2,1,4,5,7,3,6]
[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[2,1,5,7,6,4,3]=>[2,1,7,6,4,3,5]=>[2,1,4,6,3,7,5]
[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[2,1,6,5,7,4,3]=>[2,1,7,4,3,6,5]=>[2,1,4,7,6,3,5]
[[.,[.,.]],[.,[[[.,.],.],.]]]=>[2,1,5,6,7,4,3]=>[2,1,7,4,3,5,6]=>[2,1,4,7,3,5,6]
[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[2,1,4,7,6,5,3]=>[2,1,7,6,5,3,4]=>[2,1,5,3,6,7,4]
[[.,[.,.]],[[.,.],[[.,.],.]]]=>[2,1,4,6,7,5,3]=>[2,1,7,5,3,4,6]=>[2,1,5,3,7,4,6]
[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[2,1,5,4,7,6,3]=>[2,1,7,6,3,5,4]=>[2,1,6,5,3,7,4]
[[.,[.,.]],[[[.,.],.],[.,.]]]=>[2,1,4,5,7,6,3]=>[2,1,7,6,3,4,5]=>[2,1,6,3,4,7,5]
[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[2,1,6,5,4,7,3]=>[2,1,7,3,6,5,4]=>[2,1,7,5,6,3,4]
[[.,[.,.]],[[.,[[.,.],.]],.]]=>[2,1,5,6,4,7,3]=>[2,1,7,3,6,4,5]=>[2,1,7,6,4,3,5]
[[.,[.,.]],[[[.,.],[.,.]],.]]=>[2,1,4,6,5,7,3]=>[2,1,7,3,4,6,5]=>[2,1,7,3,6,4,5]
[[.,[.,.]],[[[.,[.,.]],.],.]]=>[2,1,5,4,6,7,3]=>[2,1,7,3,5,4,6]=>[2,1,7,5,3,4,6]
[[.,[.,.]],[[[[.,.],.],.],.]]=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>[2,1,7,3,4,5,6]
[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]
[[[.,.],.],[.,[.,[[.,.],.]]]]=>[1,2,6,7,5,4,3]=>[1,2,7,5,4,3,6]=>[1,2,4,5,7,3,6]
[[[.,.],.],[.,[[.,.],[.,.]]]]=>[1,2,5,7,6,4,3]=>[1,2,7,6,4,3,5]=>[1,2,4,6,3,7,5]
[[[.,.],.],[.,[[.,[.,.]],.]]]=>[1,2,6,5,7,4,3]=>[1,2,7,4,3,6,5]=>[1,2,4,7,6,3,5]
[[[.,.],.],[.,[[[.,.],.],.]]]=>[1,2,5,6,7,4,3]=>[1,2,7,4,3,5,6]=>[1,2,4,7,3,5,6]
[[[.,.],.],[[.,.],[.,[.,.]]]]=>[1,2,4,7,6,5,3]=>[1,2,7,6,5,3,4]=>[1,2,5,3,6,7,4]
[[[.,.],.],[[.,.],[[.,.],.]]]=>[1,2,4,6,7,5,3]=>[1,2,7,5,3,4,6]=>[1,2,5,3,7,4,6]
[[[.,.],.],[[.,[.,.]],[.,.]]]=>[1,2,5,4,7,6,3]=>[1,2,7,6,3,5,4]=>[1,2,6,5,3,7,4]
[[[.,.],.],[[[.,.],.],[.,.]]]=>[1,2,4,5,7,6,3]=>[1,2,7,6,3,4,5]=>[1,2,6,3,4,7,5]
[[[.,.],.],[[.,[.,[.,.]]],.]]=>[1,2,6,5,4,7,3]=>[1,2,7,3,6,5,4]=>[1,2,7,5,6,3,4]
[[[.,.],.],[[.,[[.,.],.]],.]]=>[1,2,5,6,4,7,3]=>[1,2,7,3,6,4,5]=>[1,2,7,6,4,3,5]
[[[.,.],.],[[[.,.],[.,.]],.]]=>[1,2,4,6,5,7,3]=>[1,2,7,3,4,6,5]=>[1,2,7,3,6,4,5]
[[[.,.],.],[[[.,[.,.]],.],.]]=>[1,2,5,4,6,7,3]=>[1,2,7,3,5,4,6]=>[1,2,7,5,3,4,6]
[[[.,.],.],[[[[.,.],.],.],.]]=>[1,2,4,5,6,7,3]=>[1,2,7,3,4,5,6]=>[1,2,7,3,4,5,6]
[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[2,3,1,5,6,7,4]
[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[3,2,1,6,7,5,4]=>[3,2,1,7,5,4,6]=>[2,3,1,5,7,4,6]
[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[3,2,1,5,7,6,4]=>[3,2,1,7,6,4,5]=>[2,3,1,6,4,7,5]
[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[3,2,1,6,5,7,4]=>[3,2,1,7,4,6,5]=>[2,3,1,7,6,4,5]
[[.,[.,[.,.]]],[[[.,.],.],.]]=>[3,2,1,5,6,7,4]=>[3,2,1,7,4,5,6]=>[2,3,1,7,4,5,6]
[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[2,3,1,7,6,5,4]=>[3,1,2,7,6,5,4]=>[3,1,2,5,6,7,4]
[[.,[[.,.],.]],[.,[[.,.],.]]]=>[2,3,1,6,7,5,4]=>[3,1,2,7,5,4,6]=>[3,1,2,5,7,4,6]
[[.,[[.,.],.]],[[.,.],[.,.]]]=>[2,3,1,5,7,6,4]=>[3,1,2,7,6,4,5]=>[3,1,2,6,4,7,5]
[[.,[[.,.],.]],[[.,[.,.]],.]]=>[2,3,1,6,5,7,4]=>[3,1,2,7,4,6,5]=>[3,1,2,7,6,4,5]
[[.,[[.,.],.]],[[[.,.],.],.]]=>[2,3,1,5,6,7,4]=>[3,1,2,7,4,5,6]=>[3,1,2,7,4,5,6]
[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]
[[[.,.],[.,.]],[.,[[.,.],.]]]=>[1,3,2,6,7,5,4]=>[1,3,2,7,5,4,6]=>[1,3,2,5,7,4,6]
[[[.,.],[.,.]],[[.,.],[.,.]]]=>[1,3,2,5,7,6,4]=>[1,3,2,7,6,4,5]=>[1,3,2,6,4,7,5]
[[[.,.],[.,.]],[[.,[.,.]],.]]=>[1,3,2,6,5,7,4]=>[1,3,2,7,4,6,5]=>[1,3,2,7,6,4,5]
[[[.,.],[.,.]],[[[.,.],.],.]]=>[1,3,2,5,6,7,4]=>[1,3,2,7,4,5,6]=>[1,3,2,7,4,5,6]
[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]=>[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]
[[[.,[.,.]],.],[.,[[.,.],.]]]=>[2,1,3,6,7,5,4]=>[2,1,3,7,5,4,6]=>[2,1,3,5,7,4,6]
[[[.,[.,.]],.],[[.,.],[.,.]]]=>[2,1,3,5,7,6,4]=>[2,1,3,7,6,4,5]=>[2,1,3,6,4,7,5]
[[[.,[.,.]],.],[[.,[.,.]],.]]=>[2,1,3,6,5,7,4]=>[2,1,3,7,4,6,5]=>[2,1,3,7,6,4,5]
[[[.,[.,.]],.],[[[.,.],.],.]]=>[2,1,3,5,6,7,4]=>[2,1,3,7,4,5,6]=>[2,1,3,7,4,5,6]
[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]
[[[[.,.],.],.],[.,[[.,.],.]]]=>[1,2,3,6,7,5,4]=>[1,2,3,7,5,4,6]=>[1,2,3,5,7,4,6]
[[[[.,.],.],.],[[.,.],[.,.]]]=>[1,2,3,5,7,6,4]=>[1,2,3,7,6,4,5]=>[1,2,3,6,4,7,5]
[[[[.,.],.],.],[[.,[.,.]],.]]=>[1,2,3,6,5,7,4]=>[1,2,3,7,4,6,5]=>[1,2,3,7,6,4,5]
[[[[.,.],.],.],[[[.,.],.],.]]=>[1,2,3,5,6,7,4]=>[1,2,3,7,4,5,6]=>[1,2,3,7,4,5,6]
[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[2,3,4,1,6,7,5]
[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[4,3,2,1,6,7,5]=>[4,3,2,1,7,5,6]=>[2,3,4,1,7,5,6]
[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[3,4,2,1,7,6,5]=>[4,2,1,3,7,6,5]=>[2,4,1,3,6,7,5]
[[.,[.,[[.,.],.]]],[[.,.],.]]=>[3,4,2,1,6,7,5]=>[4,2,1,3,7,5,6]=>[2,4,1,3,7,5,6]
[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[2,4,3,1,7,6,5]=>[4,3,1,2,7,6,5]=>[3,1,4,2,6,7,5]
[[.,[[.,.],[.,.]]],[[.,.],.]]=>[2,4,3,1,6,7,5]=>[4,3,1,2,7,5,6]=>[3,1,4,2,7,5,6]
[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[3,2,4,1,7,6,5]=>[4,1,3,2,7,6,5]=>[4,3,1,2,6,7,5]
[[.,[[.,[.,.]],.]],[[.,.],.]]=>[3,2,4,1,6,7,5]=>[4,1,3,2,7,5,6]=>[4,3,1,2,7,5,6]
[[.,[[[.,.],.],.]],[.,[.,.]]]=>[2,3,4,1,7,6,5]=>[4,1,2,3,7,6,5]=>[4,1,2,3,6,7,5]
[[.,[[[.,.],.],.]],[[.,.],.]]=>[2,3,4,1,6,7,5]=>[4,1,2,3,7,5,6]=>[4,1,2,3,7,5,6]
[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]
[[[.,.],[.,[.,.]]],[[.,.],.]]=>[1,4,3,2,6,7,5]=>[1,4,3,2,7,5,6]=>[1,3,4,2,7,5,6]
[[[.,.],[[.,.],.]],[.,[.,.]]]=>[1,3,4,2,7,6,5]=>[1,4,2,3,7,6,5]=>[1,4,2,3,6,7,5]
[[[.,.],[[.,.],.]],[[.,.],.]]=>[1,3,4,2,6,7,5]=>[1,4,2,3,7,5,6]=>[1,4,2,3,7,5,6]
[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]
[[[.,[.,.]],[.,.]],[[.,.],.]]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,5,6]=>[2,1,4,3,7,5,6]
[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]
[[[[.,.],.],[.,.]],[[.,.],.]]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,5,6]
[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]
[[[.,[.,[.,.]]],.],[[.,.],.]]=>[3,2,1,4,6,7,5]=>[3,2,1,4,7,5,6]=>[2,3,1,4,7,5,6]
[[[.,[[.,.],.]],.],[.,[.,.]]]=>[2,3,1,4,7,6,5]=>[3,1,2,4,7,6,5]=>[3,1,2,4,6,7,5]
[[[.,[[.,.],.]],.],[[.,.],.]]=>[2,3,1,4,6,7,5]=>[3,1,2,4,7,5,6]=>[3,1,2,4,7,5,6]
[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]
[[[[.,.],[.,.]],.],[[.,.],.]]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,5,6]
[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]
[[[[.,[.,.]],.],.],[[.,.],.]]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,5,6]=>[2,1,3,4,7,5,6]
[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]
[[[[[.,.],.],.],.],[[.,.],.]]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,5,6]
[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[2,3,4,5,1,7,6]
[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[4,5,3,2,1,7,6]=>[5,3,2,1,4,7,6]=>[2,3,5,1,4,7,6]
[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[3,5,4,2,1,7,6]=>[5,4,2,1,3,7,6]=>[2,4,1,5,3,7,6]
[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[4,3,5,2,1,7,6]=>[5,2,1,4,3,7,6]=>[2,5,4,1,3,7,6]
[[.,[.,[[[.,.],.],.]]],[.,.]]=>[3,4,5,2,1,7,6]=>[5,2,1,3,4,7,6]=>[2,5,1,3,4,7,6]
[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[2,5,4,3,1,7,6]=>[5,4,3,1,2,7,6]=>[3,1,4,5,2,7,6]
[[.,[[.,.],[[.,.],.]]],[.,.]]=>[2,4,5,3,1,7,6]=>[5,3,1,2,4,7,6]=>[3,1,5,2,4,7,6]
[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[3,2,5,4,1,7,6]=>[5,4,1,3,2,7,6]=>[4,3,1,5,2,7,6]
[[.,[[[.,.],.],[.,.]]],[.,.]]=>[2,3,5,4,1,7,6]=>[5,4,1,2,3,7,6]=>[4,1,2,5,3,7,6]
[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[4,3,2,5,1,7,6]=>[5,1,4,3,2,7,6]=>[5,3,4,1,2,7,6]
[[.,[[.,[[.,.],.]],.]],[.,.]]=>[3,4,2,5,1,7,6]=>[5,1,4,2,3,7,6]=>[5,4,2,1,3,7,6]
[[.,[[[.,.],[.,.]],.]],[.,.]]=>[2,4,3,5,1,7,6]=>[5,1,2,4,3,7,6]=>[5,1,4,2,3,7,6]
[[.,[[[.,[.,.]],.],.]],[.,.]]=>[3,2,4,5,1,7,6]=>[5,1,3,2,4,7,6]=>[5,3,1,2,4,7,6]
[[.,[[[[.,.],.],.],.]],[.,.]]=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>[5,1,2,3,4,7,6]
[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]=>[1,5,4,3,2,7,6]=>[1,3,4,5,2,7,6]
[[[.,.],[.,[[.,.],.]]],[.,.]]=>[1,4,5,3,2,7,6]=>[1,5,3,2,4,7,6]=>[1,3,5,2,4,7,6]
[[[.,.],[[.,.],[.,.]]],[.,.]]=>[1,3,5,4,2,7,6]=>[1,5,4,2,3,7,6]=>[1,4,2,5,3,7,6]
[[[.,.],[[.,[.,.]],.]],[.,.]]=>[1,4,3,5,2,7,6]=>[1,5,2,4,3,7,6]=>[1,5,4,2,3,7,6]
[[[.,.],[[[.,.],.],.]],[.,.]]=>[1,3,4,5,2,7,6]=>[1,5,2,3,4,7,6]=>[1,5,2,3,4,7,6]
[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]
[[[.,[.,.]],[[.,.],.]],[.,.]]=>[2,1,4,5,3,7,6]=>[2,1,5,3,4,7,6]=>[2,1,5,3,4,7,6]
[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]
[[[[.,.],.],[[.,.],.]],[.,.]]=>[1,2,4,5,3,7,6]=>[1,2,5,3,4,7,6]=>[1,2,5,3,4,7,6]
[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]
[[[.,[[.,.],.]],[.,.]],[.,.]]=>[2,3,1,5,4,7,6]=>[3,1,2,5,4,7,6]=>[3,1,2,5,4,7,6]
[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]
[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]
[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]
[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]=>[4,3,2,1,5,7,6]=>[2,3,4,1,5,7,6]
[[[.,[.,[[.,.],.]]],.],[.,.]]=>[3,4,2,1,5,7,6]=>[4,2,1,3,5,7,6]=>[2,4,1,3,5,7,6]
[[[.,[[.,.],[.,.]]],.],[.,.]]=>[2,4,3,1,5,7,6]=>[4,3,1,2,5,7,6]=>[3,1,4,2,5,7,6]
[[[.,[[.,[.,.]],.]],.],[.,.]]=>[3,2,4,1,5,7,6]=>[4,1,3,2,5,7,6]=>[4,3,1,2,5,7,6]
[[[.,[[[.,.],.],.]],.],[.,.]]=>[2,3,4,1,5,7,6]=>[4,1,2,3,5,7,6]=>[4,1,2,3,5,7,6]
[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]
[[[[.,.],[[.,.],.]],.],[.,.]]=>[1,3,4,2,5,7,6]=>[1,4,2,3,5,7,6]=>[1,4,2,3,5,7,6]
[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]
[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]
[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]
[[[[.,[[.,.],.]],.],.],[.,.]]=>[2,3,1,4,5,7,6]=>[3,1,2,4,5,7,6]=>[3,1,2,4,5,7,6]
[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]
[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]
[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]
[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]
[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[6,4,3,2,1,5,7]=>[2,3,4,6,1,5,7]
[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[4,6,5,3,2,1,7]=>[6,5,3,2,1,4,7]=>[2,3,5,1,6,4,7]
[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[6,3,2,1,5,4,7]=>[2,3,6,5,1,4,7]
[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[6,3,2,1,4,5,7]=>[2,3,6,1,4,5,7]
[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[3,6,5,4,2,1,7]=>[6,5,4,2,1,3,7]=>[2,4,1,5,6,3,7]
[[.,[.,[[.,.],[[.,.],.]]]],.]=>[3,5,6,4,2,1,7]=>[6,4,2,1,3,5,7]=>[2,4,1,6,3,5,7]
[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[4,3,6,5,2,1,7]=>[6,5,2,1,4,3,7]=>[2,5,4,1,6,3,7]
[[.,[.,[[[.,.],.],[.,.]]]],.]=>[3,4,6,5,2,1,7]=>[6,5,2,1,3,4,7]=>[2,5,1,3,6,4,7]
[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[6,2,1,5,4,3,7]=>[2,6,4,5,1,3,7]
[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[6,2,1,5,3,4,7]=>[2,6,5,3,1,4,7]
[[.,[.,[[[.,.],[.,.]],.]]],.]=>[3,5,4,6,2,1,7]=>[6,2,1,3,5,4,7]=>[2,6,1,5,3,4,7]
[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[6,2,1,4,3,5,7]=>[2,6,4,1,3,5,7]
[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]
[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[2,6,5,4,3,1,7]=>[6,5,4,3,1,2,7]=>[3,1,4,5,6,2,7]
[[.,[[.,.],[.,[[.,.],.]]]],.]=>[2,5,6,4,3,1,7]=>[6,4,3,1,2,5,7]=>[3,1,4,6,2,5,7]
[[.,[[.,.],[[.,.],[.,.]]]],.]=>[2,4,6,5,3,1,7]=>[6,5,3,1,2,4,7]=>[3,1,5,2,6,4,7]
[[.,[[.,.],[[.,[.,.]],.]]],.]=>[2,5,4,6,3,1,7]=>[6,3,1,2,5,4,7]=>[3,1,6,5,2,4,7]
[[.,[[.,.],[[[.,.],.],.]]],.]=>[2,4,5,6,3,1,7]=>[6,3,1,2,4,5,7]=>[3,1,6,2,4,5,7]
[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[3,2,6,5,4,1,7]=>[6,5,4,1,3,2,7]=>[4,3,1,5,6,2,7]
[[.,[[.,[.,.]],[[.,.],.]]],.]=>[3,2,5,6,4,1,7]=>[6,4,1,3,2,5,7]=>[4,3,1,6,2,5,7]
[[.,[[[.,.],.],[.,[.,.]]]],.]=>[2,3,6,5,4,1,7]=>[6,5,4,1,2,3,7]=>[4,1,2,5,6,3,7]
[[.,[[[.,.],.],[[.,.],.]]],.]=>[2,3,5,6,4,1,7]=>[6,4,1,2,3,5,7]=>[4,1,2,6,3,5,7]
[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[4,3,2,6,5,1,7]=>[6,5,1,4,3,2,7]=>[5,3,4,1,6,2,7]
[[.,[[.,[[.,.],.]],[.,.]]],.]=>[3,4,2,6,5,1,7]=>[6,5,1,4,2,3,7]=>[5,4,2,1,6,3,7]
[[.,[[[.,.],[.,.]],[.,.]]],.]=>[2,4,3,6,5,1,7]=>[6,5,1,2,4,3,7]=>[5,1,4,2,6,3,7]
[[.,[[[.,[.,.]],.],[.,.]]],.]=>[3,2,4,6,5,1,7]=>[6,5,1,3,2,4,7]=>[5,3,1,2,6,4,7]
[[.,[[[[.,.],.],.],[.,.]]],.]=>[2,3,4,6,5,1,7]=>[6,5,1,2,3,4,7]=>[5,1,2,3,6,4,7]
[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[6,1,5,4,3,2,7]=>[6,3,4,5,1,2,7]
[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[6,1,5,3,2,4,7]=>[6,3,5,2,1,4,7]
[[.,[[.,[[.,.],[.,.]]],.]],.]=>[3,5,4,2,6,1,7]=>[6,1,5,4,2,3,7]=>[6,4,2,5,1,3,7]
[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[6,1,5,2,4,3,7]=>[6,5,4,2,1,3,7]
[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[6,1,5,2,3,4,7]=>[6,5,2,3,1,4,7]
[[.,[[[.,.],[.,[.,.]]],.]],.]=>[2,5,4,3,6,1,7]=>[6,1,2,5,4,3,7]=>[6,1,4,5,2,3,7]
[[.,[[[.,.],[[.,.],.]],.]],.]=>[2,4,5,3,6,1,7]=>[6,1,2,5,3,4,7]=>[6,1,5,3,2,4,7]
[[.,[[[.,[.,.]],[.,.]],.]],.]=>[3,2,5,4,6,1,7]=>[6,1,3,2,5,4,7]=>[6,3,1,5,2,4,7]
[[.,[[[[.,.],.],[.,.]],.]],.]=>[2,3,5,4,6,1,7]=>[6,1,2,3,5,4,7]=>[6,1,2,5,3,4,7]
[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[6,1,4,3,2,5,7]=>[6,3,4,1,2,5,7]
[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[6,1,4,2,3,5,7]=>[6,4,2,1,3,5,7]
[[.,[[[[.,.],[.,.]],.],.]],.]=>[2,4,3,5,6,1,7]=>[6,1,2,4,3,5,7]=>[6,1,4,2,3,5,7]
[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[6,1,3,2,4,5,7]=>[6,3,1,2,4,5,7]
[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]
[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]=>[1,6,5,4,3,2,7]=>[1,3,4,5,6,2,7]
[[[.,.],[.,[.,[[.,.],.]]]],.]=>[1,5,6,4,3,2,7]=>[1,6,4,3,2,5,7]=>[1,3,4,6,2,5,7]
[[[.,.],[.,[[.,.],[.,.]]]],.]=>[1,4,6,5,3,2,7]=>[1,6,5,3,2,4,7]=>[1,3,5,2,6,4,7]
[[[.,.],[.,[[.,[.,.]],.]]],.]=>[1,5,4,6,3,2,7]=>[1,6,3,2,5,4,7]=>[1,3,6,5,2,4,7]
[[[.,.],[.,[[[.,.],.],.]]],.]=>[1,4,5,6,3,2,7]=>[1,6,3,2,4,5,7]=>[1,3,6,2,4,5,7]
[[[.,.],[[.,.],[.,[.,.]]]],.]=>[1,3,6,5,4,2,7]=>[1,6,5,4,2,3,7]=>[1,4,2,5,6,3,7]
[[[.,.],[[.,.],[[.,.],.]]],.]=>[1,3,5,6,4,2,7]=>[1,6,4,2,3,5,7]=>[1,4,2,6,3,5,7]
[[[.,.],[[.,[.,.]],[.,.]]],.]=>[1,4,3,6,5,2,7]=>[1,6,5,2,4,3,7]=>[1,5,4,2,6,3,7]
[[[.,.],[[[.,.],.],[.,.]]],.]=>[1,3,4,6,5,2,7]=>[1,6,5,2,3,4,7]=>[1,5,2,3,6,4,7]
[[[.,.],[[.,[.,[.,.]]],.]],.]=>[1,5,4,3,6,2,7]=>[1,6,2,5,4,3,7]=>[1,6,4,5,2,3,7]
[[[.,.],[[.,[[.,.],.]],.]],.]=>[1,4,5,3,6,2,7]=>[1,6,2,5,3,4,7]=>[1,6,5,3,2,4,7]
[[[.,.],[[[.,.],[.,.]],.]],.]=>[1,3,5,4,6,2,7]=>[1,6,2,3,5,4,7]=>[1,6,2,5,3,4,7]
[[[.,.],[[[.,[.,.]],.],.]],.]=>[1,4,3,5,6,2,7]=>[1,6,2,4,3,5,7]=>[1,6,4,2,3,5,7]
[[[.,.],[[[[.,.],.],.],.]],.]=>[1,3,4,5,6,2,7]=>[1,6,2,3,4,5,7]=>[1,6,2,3,4,5,7]
[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]=>[2,1,6,5,4,3,7]=>[2,1,4,5,6,3,7]
[[[.,[.,.]],[.,[[.,.],.]]],.]=>[2,1,5,6,4,3,7]=>[2,1,6,4,3,5,7]=>[2,1,4,6,3,5,7]
[[[.,[.,.]],[[.,.],[.,.]]],.]=>[2,1,4,6,5,3,7]=>[2,1,6,5,3,4,7]=>[2,1,5,3,6,4,7]
[[[.,[.,.]],[[.,[.,.]],.]],.]=>[2,1,5,4,6,3,7]=>[2,1,6,3,5,4,7]=>[2,1,6,5,3,4,7]
[[[.,[.,.]],[[[.,.],.],.]],.]=>[2,1,4,5,6,3,7]=>[2,1,6,3,4,5,7]=>[2,1,6,3,4,5,7]
[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]=>[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]
[[[[.,.],.],[.,[[.,.],.]]],.]=>[1,2,5,6,4,3,7]=>[1,2,6,4,3,5,7]=>[1,2,4,6,3,5,7]
[[[[.,.],.],[[.,.],[.,.]]],.]=>[1,2,4,6,5,3,7]=>[1,2,6,5,3,4,7]=>[1,2,5,3,6,4,7]
[[[[.,.],.],[[.,[.,.]],.]],.]=>[1,2,5,4,6,3,7]=>[1,2,6,3,5,4,7]=>[1,2,6,5,3,4,7]
[[[[.,.],.],[[[.,.],.],.]],.]=>[1,2,4,5,6,3,7]=>[1,2,6,3,4,5,7]=>[1,2,6,3,4,5,7]
[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]=>[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]
[[[.,[.,[.,.]]],[[.,.],.]],.]=>[3,2,1,5,6,4,7]=>[3,2,1,6,4,5,7]=>[2,3,1,6,4,5,7]
[[[.,[[.,.],.]],[.,[.,.]]],.]=>[2,3,1,6,5,4,7]=>[3,1,2,6,5,4,7]=>[3,1,2,5,6,4,7]
[[[.,[[.,.],.]],[[.,.],.]],.]=>[2,3,1,5,6,4,7]=>[3,1,2,6,4,5,7]=>[3,1,2,6,4,5,7]
[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]
[[[[.,.],[.,.]],[[.,.],.]],.]=>[1,3,2,5,6,4,7]=>[1,3,2,6,4,5,7]=>[1,3,2,6,4,5,7]
[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]
[[[[.,[.,.]],.],[[.,.],.]],.]=>[2,1,3,5,6,4,7]=>[2,1,3,6,4,5,7]=>[2,1,3,6,4,5,7]
[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]
[[[[[.,.],.],.],[[.,.],.]],.]=>[1,2,3,5,6,4,7]=>[1,2,3,6,4,5,7]=>[1,2,3,6,4,5,7]
[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]=>[4,3,2,1,6,5,7]=>[2,3,4,1,6,5,7]
[[[.,[.,[[.,.],.]]],[.,.]],.]=>[3,4,2,1,6,5,7]=>[4,2,1,3,6,5,7]=>[2,4,1,3,6,5,7]
[[[.,[[.,.],[.,.]]],[.,.]],.]=>[2,4,3,1,6,5,7]=>[4,3,1,2,6,5,7]=>[3,1,4,2,6,5,7]
[[[.,[[.,[.,.]],.]],[.,.]],.]=>[3,2,4,1,6,5,7]=>[4,1,3,2,6,5,7]=>[4,3,1,2,6,5,7]
[[[.,[[[.,.],.],.]],[.,.]],.]=>[2,3,4,1,6,5,7]=>[4,1,2,3,6,5,7]=>[4,1,2,3,6,5,7]
[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]
[[[[.,.],[[.,.],.]],[.,.]],.]=>[1,3,4,2,6,5,7]=>[1,4,2,3,6,5,7]=>[1,4,2,3,6,5,7]
[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]
[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]
[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]
[[[[.,[[.,.],.]],.],[.,.]],.]=>[2,3,1,4,6,5,7]=>[3,1,2,4,6,5,7]=>[3,1,2,4,6,5,7]
[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]
[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]
[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]
[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]
[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[5,3,2,1,4,6,7]=>[2,3,5,1,4,6,7]
[[[.,[.,[[.,.],[.,.]]]],.],.]=>[3,5,4,2,1,6,7]=>[5,4,2,1,3,6,7]=>[2,4,1,5,3,6,7]
[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[5,2,1,4,3,6,7]=>[2,5,4,1,3,6,7]
[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]
[[[.,[[.,.],[.,[.,.]]]],.],.]=>[2,5,4,3,1,6,7]=>[5,4,3,1,2,6,7]=>[3,1,4,5,2,6,7]
[[[.,[[.,.],[[.,.],.]]],.],.]=>[2,4,5,3,1,6,7]=>[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]
[[[.,[[.,[.,.]],[.,.]]],.],.]=>[3,2,5,4,1,6,7]=>[5,4,1,3,2,6,7]=>[4,3,1,5,2,6,7]
[[[.,[[[.,.],.],[.,.]]],.],.]=>[2,3,5,4,1,6,7]=>[5,4,1,2,3,6,7]=>[4,1,2,5,3,6,7]
[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[5,1,4,3,2,6,7]=>[5,3,4,1,2,6,7]
[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[5,1,4,2,3,6,7]=>[5,4,2,1,3,6,7]
[[[.,[[[.,.],[.,.]],.]],.],.]=>[2,4,3,5,1,6,7]=>[5,1,2,4,3,6,7]=>[5,1,4,2,3,6,7]
[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[5,1,3,2,4,6,7]=>[5,3,1,2,4,6,7]
[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]
[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]=>[1,5,4,3,2,6,7]=>[1,3,4,5,2,6,7]
[[[[.,.],[.,[[.,.],.]]],.],.]=>[1,4,5,3,2,6,7]=>[1,5,3,2,4,6,7]=>[1,3,5,2,4,6,7]
[[[[.,.],[[.,.],[.,.]]],.],.]=>[1,3,5,4,2,6,7]=>[1,5,4,2,3,6,7]=>[1,4,2,5,3,6,7]
[[[[.,.],[[.,[.,.]],.]],.],.]=>[1,4,3,5,2,6,7]=>[1,5,2,4,3,6,7]=>[1,5,4,2,3,6,7]
[[[[.,.],[[[.,.],.],.]],.],.]=>[1,3,4,5,2,6,7]=>[1,5,2,3,4,6,7]=>[1,5,2,3,4,6,7]
[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]=>[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]
[[[[.,[.,.]],[[.,.],.]],.],.]=>[2,1,4,5,3,6,7]=>[2,1,5,3,4,6,7]=>[2,1,5,3,4,6,7]
[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]
[[[[[.,.],.],[[.,.],.]],.],.]=>[1,2,4,5,3,6,7]=>[1,2,5,3,4,6,7]=>[1,2,5,3,4,6,7]
[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]
[[[[.,[[.,.],.]],[.,.]],.],.]=>[2,3,1,5,4,6,7]=>[3,1,2,5,4,6,7]=>[3,1,2,5,4,6,7]
[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]
[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]
[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]
[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]
[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]
[[[[.,[[.,.],[.,.]]],.],.],.]=>[2,4,3,1,5,6,7]=>[4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]
[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[4,1,3,2,5,6,7]=>[4,3,1,2,5,6,7]
[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]
[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]=>[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]
[[[[[.,.],[[.,.],.]],.],.],.]=>[1,3,4,2,5,6,7]=>[1,4,2,3,5,6,7]=>[1,4,2,3,5,6,7]
[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]
[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]
[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]
[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]
[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]
[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]
[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]
[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]
[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[8,6,5,4,3,2,1,7]=>[2,3,4,5,6,8,1,7]
[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[8,5,4,3,2,1,7,6]=>[2,3,4,5,8,7,1,6]
[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[8,5,4,3,2,1,6,7]=>[2,3,4,5,8,1,6,7]
[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[5,8,7,6,4,3,2,1]=>[8,7,6,4,3,2,1,5]=>[2,3,4,6,1,7,8,5]
[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[6,5,8,7,4,3,2,1]=>[8,7,4,3,2,1,6,5]=>[2,3,4,7,6,1,8,5]
[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[8,4,3,2,1,7,6,5]=>[2,3,4,8,6,7,1,5]
[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[8,4,3,2,1,6,5,7]=>[2,3,4,8,6,1,5,7]
[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[8,4,3,2,1,5,6,7]=>[2,3,4,8,1,5,6,7]
[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[4,8,7,6,5,3,2,1]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]
[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[8,3,2,1,7,6,5,4]=>[2,3,8,5,6,7,1,4]
[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[8,3,2,1,7,4,6,5]=>[2,3,8,7,6,4,1,5]
[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[4,7,6,5,8,3,2,1]=>[8,3,2,1,4,7,6,5]=>[2,3,8,1,6,7,4,5]
[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[8,3,2,1,4,5,6,7]=>[2,3,8,1,4,5,6,7]
[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[3,7,6,8,5,4,2,1]=>[8,5,4,2,1,3,7,6]=>[2,4,1,5,8,7,3,6]
[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[3,5,8,7,6,4,2,1]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]
[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]=>[3,5,6,8,7,4,2,1]=>[8,7,4,2,1,3,5,6]=>[2,4,1,7,3,5,8,6]
[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[3,5,6,7,8,4,2,1]=>[8,4,2,1,3,5,6,7]=>[2,4,1,8,3,5,6,7]
[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[3,4,8,7,6,5,2,1]=>[8,7,6,5,2,1,3,4]=>[2,5,1,3,6,7,8,4]
[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[3,4,5,8,7,6,2,1]=>[8,7,6,2,1,3,4,5]=>[2,6,1,3,4,7,8,5]
[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[4,3,6,5,8,7,2,1]=>[8,7,2,1,4,3,6,5]=>[2,7,4,1,6,3,8,5]
[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[8,2,1,7,6,5,4,3]=>[2,8,4,5,6,7,1,3]
[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[5,7,6,4,3,8,2,1]=>[8,2,1,7,6,4,3,5]=>[2,8,4,6,3,7,1,5]
[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[8,2,1,7,3,5,4,6]=>[2,8,7,5,3,4,1,6]
[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[8,2,1,7,3,4,5,6]=>[2,8,7,3,4,5,1,6]
[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[8,2,1,4,3,5,6,7]=>[2,8,4,1,3,5,6,7]
[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[2,7,8,6,5,4,3,1]=>[8,6,5,4,3,1,2,7]=>[3,1,4,5,6,8,2,7]
[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[2,6,8,7,5,4,3,1]=>[8,7,5,4,3,1,2,6]=>[3,1,4,5,7,2,8,6]
[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[2,5,6,7,8,4,3,1]=>[8,4,3,1,2,5,6,7]=>[3,1,4,8,2,5,6,7]
[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[2,4,8,7,6,5,3,1]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]
[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[2,4,6,8,7,5,3,1]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]
[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[2,7,6,5,4,8,3,1]=>[8,3,1,2,7,6,5,4]=>[3,1,8,5,6,7,2,4]
[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[2,3,5,6,8,7,4,1]=>[8,7,4,1,2,3,5,6]=>[4,1,2,7,3,5,8,6]
[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[2,3,5,6,7,8,4,1]=>[8,4,1,2,3,5,6,7]=>[4,1,2,8,3,5,6,7]
[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[4,3,2,8,7,6,5,1]=>[8,7,6,5,1,4,3,2]=>[5,3,4,1,6,7,8,2]
[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[3,4,2,8,7,6,5,1]=>[8,7,6,5,1,4,2,3]=>[5,4,2,1,6,7,8,3]
[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[2,4,3,8,7,6,5,1]=>[8,7,6,5,1,2,4,3]=>[5,1,4,2,6,7,8,3]
[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[3,2,4,8,7,6,5,1]=>[8,7,6,5,1,3,2,4]=>[5,3,1,2,6,7,8,4]
[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[2,3,4,8,7,6,5,1]=>[8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,4]
[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[5,4,3,2,8,7,6,1]=>[8,7,6,1,5,4,3,2]=>[6,3,4,5,1,7,8,2]
[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[5,4,3,2,7,8,6,1]=>[8,6,1,5,4,3,2,7]=>[6,3,4,5,1,8,2,7]
[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[2,5,4,3,8,7,6,1]=>[8,7,6,1,2,5,4,3]=>[6,1,4,5,2,7,8,3]
[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]=>[2,5,4,3,7,8,6,1]=>[8,6,1,2,5,4,3,7]=>[6,1,4,5,2,8,3,7]
[.,[[[.,.],[[.,.],.]],[[.,.],.]]]=>[2,4,5,3,7,8,6,1]=>[8,6,1,2,5,3,4,7]=>[6,1,5,3,2,8,4,7]
[.,[[[.,[[.,.],.]],.],[[.,.],.]]]=>[3,4,2,5,7,8,6,1]=>[8,6,1,4,2,3,5,7]=>[6,4,2,1,3,8,5,7]
[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[4,3,6,5,2,8,7,1]=>[8,7,1,6,5,2,4,3]=>[7,5,4,2,6,1,8,3]
[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[3,2,6,5,4,8,7,1]=>[8,7,1,3,2,6,5,4]=>[7,3,1,5,6,2,8,4]
[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[2,4,3,6,5,8,7,1]=>[8,7,1,2,4,3,6,5]=>[7,1,4,2,6,3,8,5]
[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]=>[5,4,3,2,6,8,7,1]=>[8,7,1,5,4,3,2,6]=>[7,3,4,5,1,2,8,6]
[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[2,5,4,3,6,8,7,1]=>[8,7,1,2,5,4,3,6]=>[7,1,4,5,2,3,8,6]
[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[2,4,3,5,6,8,7,1]=>[8,7,1,2,4,3,5,6]=>[7,1,4,2,3,5,8,6]
[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[2,3,4,5,6,8,7,1]=>[8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,6]
[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[8,1,7,6,5,4,3,2]=>[8,3,4,5,6,7,1,2]
[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[8,1,7,5,4,3,2,6]=>[8,3,4,5,7,2,1,6]
[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[8,1,7,4,3,2,6,5]=>[8,3,4,7,6,2,1,5]
[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[8,1,7,3,2,4,5,6]=>[8,3,7,2,4,5,1,6]
[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[8,1,7,2,6,5,4,3]=>[8,7,4,5,6,2,1,3]
[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[8,1,7,2,6,3,5,4]=>[8,7,6,5,3,2,1,4]
[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[4,3,6,5,7,2,8,1]=>[8,1,7,2,4,3,6,5]=>[8,7,4,2,6,3,1,5]
[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[2,5,4,7,6,3,8,1]=>[8,1,2,7,6,3,5,4]=>[8,1,6,5,3,7,2,4]
[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[2,5,4,6,7,3,8,1]=>[8,1,2,7,3,5,4,6]=>[8,1,7,5,3,4,2,6]
[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[3,2,6,5,7,4,8,1]=>[8,1,3,2,7,4,6,5]=>[8,3,1,7,6,4,2,5]
[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]=>[4,3,2,7,6,5,8,1]=>[8,1,4,3,2,7,6,5]=>[8,3,4,1,6,7,2,5]
[.,[[[.,[[.,.],.]],[.,[.,.]]],.]]=>[3,4,2,7,6,5,8,1]=>[8,1,4,2,3,7,6,5]=>[8,4,2,1,6,7,3,5]
[.,[[[.,[[.,.],.]],[[.,.],.]],.]]=>[3,4,2,6,7,5,8,1]=>[8,1,4,2,3,7,5,6]=>[8,4,2,1,7,5,3,6]
[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[2,4,3,7,6,5,8,1]=>[8,1,2,4,3,7,6,5]=>[8,1,4,2,6,7,3,5]
[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[3,2,4,7,6,5,8,1]=>[8,1,3,2,4,7,6,5]=>[8,3,1,2,6,7,4,5]
[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[2,3,4,7,6,5,8,1]=>[8,1,2,3,4,7,6,5]=>[8,1,2,3,6,7,4,5]
[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[5,4,3,2,7,6,8,1]=>[8,1,5,4,3,2,7,6]=>[8,3,4,5,1,7,2,6]
[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[4,3,5,2,7,6,8,1]=>[8,1,5,2,4,3,7,6]=>[8,5,4,2,1,7,3,6]
[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[2,5,4,3,7,6,8,1]=>[8,1,2,5,4,3,7,6]=>[8,1,4,5,2,7,3,6]
[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[3,2,5,4,7,6,8,1]=>[8,1,3,2,5,4,7,6]=>[8,3,1,5,2,7,4,6]
[.,[[[[[.,.],.],[.,.]],[.,.]],.]]=>[2,3,5,4,7,6,8,1]=>[8,1,2,3,5,4,7,6]=>[8,1,2,5,3,7,4,6]
[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[3,2,4,5,7,6,8,1]=>[8,1,3,2,4,5,7,6]=>[8,3,1,2,4,7,5,6]
[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[2,4,3,6,5,7,8,1]=>[8,1,2,4,3,6,5,7]=>[8,1,4,2,6,3,5,7]
[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[8,1,5,4,3,2,6,7]=>[8,3,4,5,1,2,6,7]
[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[8,1,5,2,3,4,6,7]=>[8,5,2,3,1,4,6,7]
[.,[[[[[.,.],[.,[.,.]]],.],.],.]]=>[2,5,4,3,6,7,8,1]=>[8,1,2,5,4,3,6,7]=>[8,1,4,5,2,3,6,7]
[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[8,1,4,3,2,5,6,7]=>[8,3,4,1,2,5,6,7]
[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[8,1,4,2,3,5,6,7]=>[8,4,2,1,3,5,6,7]
[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[8,1,3,2,4,5,6,7]=>[8,3,1,2,4,5,6,7]
[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]
[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,2]
[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[1,7,8,6,5,4,3,2]=>[1,8,6,5,4,3,2,7]=>[1,3,4,5,6,8,2,7]
[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[1,6,8,7,5,4,3,2]=>[1,8,7,5,4,3,2,6]=>[1,3,4,5,7,2,8,6]
[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[1,7,6,8,5,4,3,2]=>[1,8,5,4,3,2,7,6]=>[1,3,4,5,8,7,2,6]
[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[1,6,7,8,5,4,3,2]=>[1,8,5,4,3,2,6,7]=>[1,3,4,5,8,2,6,7]
[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[1,5,8,7,6,4,3,2]=>[1,8,7,6,4,3,2,5]=>[1,3,4,6,2,7,8,5]
[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[1,7,6,5,8,4,3,2]=>[1,8,4,3,2,7,6,5]=>[1,3,4,8,6,7,2,5]
[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[1,5,6,7,8,4,3,2]=>[1,8,4,3,2,5,6,7]=>[1,3,4,8,2,5,6,7]
[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[1,4,8,7,6,5,3,2]=>[1,8,7,6,5,3,2,4]=>[1,3,5,2,6,7,8,4]
[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[1,4,7,8,6,5,3,2]=>[1,8,6,5,3,2,4,7]=>[1,3,5,2,6,8,4,7]
[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[1,3,5,7,8,6,4,2]=>[1,8,6,4,2,3,5,7]=>[1,4,2,6,3,8,5,7]
[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[1,3,6,5,7,8,4,2]=>[1,8,4,2,3,6,5,7]=>[1,4,2,8,6,3,5,7]
[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[1,3,5,6,7,8,4,2]=>[1,8,4,2,3,5,6,7]=>[1,4,2,8,3,5,6,7]
[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[1,4,3,8,7,6,5,2]=>[1,8,7,6,5,2,4,3]=>[1,5,4,2,6,7,8,3]
[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[1,4,3,7,8,6,5,2]=>[1,8,6,5,2,4,3,7]=>[1,5,4,2,6,8,3,7]
[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]=>[1,4,3,7,6,8,5,2]=>[1,8,5,2,4,3,7,6]=>[1,5,4,2,8,7,3,6]
[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[1,3,4,8,7,6,5,2]=>[1,8,7,6,5,2,3,4]=>[1,5,2,3,6,7,8,4]
[[.,.],[[[.,.],.],[[.,[.,.]],.]]]=>[1,3,4,7,6,8,5,2]=>[1,8,5,2,3,4,7,6]=>[1,5,2,3,8,7,4,6]
[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[1,3,4,5,7,8,6,2]=>[1,8,6,2,3,4,5,7]=>[1,6,2,3,4,8,5,7]
[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[1,6,5,4,3,8,7,2]=>[1,8,7,2,6,5,4,3]=>[1,7,4,5,6,2,8,3]
[[.,.],[[.,[.,[[.,.],.]]],[.,.]]]=>[1,5,6,4,3,8,7,2]=>[1,8,7,2,6,4,3,5]=>[1,7,4,6,3,2,8,5]
[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]=>[1,4,3,6,5,8,7,2]=>[1,8,7,2,4,3,6,5]=>[1,7,4,2,6,3,8,5]
[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[1,3,4,5,6,8,7,2]=>[1,8,7,2,3,4,5,6]=>[1,7,2,3,4,5,8,6]
[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[1,5,4,3,6,7,8,2]=>[1,8,2,5,4,3,6,7]=>[1,8,4,5,2,3,6,7]
[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[1,4,5,3,6,7,8,2]=>[1,8,2,5,3,4,6,7]=>[1,8,5,3,2,4,6,7]
[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[1,4,3,5,6,7,8,2]=>[1,8,2,4,3,5,6,7]=>[1,8,4,2,3,5,6,7]
[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>[1,8,2,3,4,5,6,7]
[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,3]
[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]=>[2,1,6,7,8,5,4,3]=>[2,1,8,5,4,3,6,7]=>[2,1,4,5,8,3,6,7]
[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[2,1,6,5,8,7,4,3]=>[2,1,8,7,4,3,6,5]=>[2,1,4,7,6,3,8,5]
[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[2,1,7,6,5,8,4,3]=>[2,1,8,4,3,7,6,5]=>[2,1,4,8,6,7,3,5]
[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]=>[2,1,6,7,5,8,4,3]=>[2,1,8,4,3,7,5,6]=>[2,1,4,8,7,5,3,6]
[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[2,1,6,5,7,8,4,3]=>[2,1,8,4,3,6,5,7]=>[2,1,4,8,6,3,5,7]
[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[2,1,5,6,7,8,4,3]=>[2,1,8,4,3,5,6,7]=>[2,1,4,8,3,5,6,7]
[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]=>[2,1,4,8,7,6,5,3]=>[2,1,8,7,6,5,3,4]=>[2,1,5,3,6,7,8,4]
[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[2,1,4,7,8,6,5,3]=>[2,1,8,6,5,3,4,7]=>[2,1,5,3,6,8,4,7]
[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]=>[2,1,4,5,8,7,6,3]=>[2,1,8,7,6,3,4,5]=>[2,1,6,3,4,7,8,5]
[[.,[.,.]],[[[.,.],.],[[.,.],.]]]=>[2,1,4,5,7,8,6,3]=>[2,1,8,6,3,4,5,7]=>[2,1,6,3,4,8,5,7]
[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[2,1,4,6,5,8,7,3]=>[2,1,8,7,3,4,6,5]=>[2,1,7,3,6,4,8,5]
[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[2,1,6,5,7,4,8,3]=>[2,1,8,3,7,4,6,5]=>[2,1,8,7,6,4,3,5]
[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[2,1,5,4,7,6,8,3]=>[2,1,8,3,5,4,7,6]=>[2,1,8,5,3,7,4,6]
[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>[2,1,8,3,4,5,6,7]
[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[1,2,6,7,8,5,4,3]=>[1,2,8,5,4,3,6,7]=>[1,2,4,5,8,3,6,7]
[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[1,2,5,6,7,8,4,3]=>[1,2,8,4,3,5,6,7]=>[1,2,4,8,3,5,6,7]
[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[1,2,4,8,7,6,5,3]=>[1,2,8,7,6,5,3,4]=>[1,2,5,3,6,7,8,4]
[[[.,.],.],[[.,.],[.,[[.,.],.]]]]=>[1,2,4,7,8,6,5,3]=>[1,2,8,6,5,3,4,7]=>[1,2,5,3,6,8,4,7]
[[[.,.],.],[[.,.],[[[.,.],.],.]]]=>[1,2,4,6,7,8,5,3]=>[1,2,8,5,3,4,6,7]=>[1,2,5,3,8,4,6,7]
[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[1,2,6,5,4,7,8,3]=>[1,2,8,3,6,5,4,7]=>[1,2,8,5,6,3,4,7]
[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[1,2,5,6,4,7,8,3]=>[1,2,8,3,6,4,5,7]=>[1,2,8,6,4,3,5,7]
[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[1,2,5,4,6,7,8,3]=>[1,2,8,3,5,4,6,7]=>[1,2,8,5,3,4,6,7]
[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[1,2,4,5,6,7,8,3]=>[1,2,8,3,4,5,6,7]=>[1,2,8,3,4,5,6,7]
[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[2,3,1,5,6,7,8,4]
[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[3,2,1,7,8,6,5,4]=>[3,2,1,8,6,5,4,7]=>[2,3,1,5,6,8,4,7]
[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[3,2,1,6,8,7,5,4]=>[3,2,1,8,7,5,4,6]=>[2,3,1,5,7,4,8,6]
[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[3,2,1,7,6,8,5,4]=>[3,2,1,8,5,4,7,6]=>[2,3,1,5,8,7,4,6]
[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[3,2,1,6,7,8,5,4]=>[3,2,1,8,5,4,6,7]=>[2,3,1,5,8,4,6,7]
[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[3,2,1,5,8,7,6,4]=>[3,2,1,8,7,6,4,5]=>[2,3,1,6,4,7,8,5]
[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[3,2,1,5,7,8,6,4]=>[3,2,1,8,6,4,5,7]=>[2,3,1,6,4,8,5,7]
[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[3,2,1,6,5,8,7,4]=>[3,2,1,8,7,4,6,5]=>[2,3,1,7,6,4,8,5]
[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[3,2,1,5,6,8,7,4]=>[3,2,1,8,7,4,5,6]=>[2,3,1,7,4,5,8,6]
[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[3,2,1,7,6,5,8,4]=>[3,2,1,8,4,7,6,5]=>[2,3,1,8,6,7,4,5]
[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[3,2,1,6,7,5,8,4]=>[3,2,1,8,4,7,5,6]=>[2,3,1,8,7,5,4,6]
[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[3,2,1,5,7,6,8,4]=>[3,2,1,8,4,5,7,6]=>[2,3,1,8,4,7,5,6]
[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[3,2,1,6,5,7,8,4]=>[3,2,1,8,4,6,5,7]=>[2,3,1,8,6,4,5,7]
[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[3,2,1,5,6,7,8,4]=>[3,2,1,8,4,5,6,7]=>[2,3,1,8,4,5,6,7]
[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[2,3,1,8,7,6,5,4]=>[3,1,2,8,7,6,5,4]=>[3,1,2,5,6,7,8,4]
[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]=>[1,3,2,8,7,6,5,4]=>[1,3,2,5,6,7,8,4]
[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]=>[2,1,3,8,7,6,5,4]=>[2,1,3,5,6,7,8,4]
[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]=>[1,2,3,8,7,6,5,4]=>[1,2,3,5,6,7,8,4]
[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[1,2,3,7,8,6,5,4]=>[1,2,3,8,6,5,4,7]=>[1,2,3,5,6,8,4,7]
[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[1,2,3,6,8,7,5,4]=>[1,2,3,8,7,5,4,6]=>[1,2,3,5,7,4,8,6]
[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[1,2,3,7,6,8,5,4]=>[1,2,3,8,5,4,7,6]=>[1,2,3,5,8,7,4,6]
[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[1,2,3,6,7,8,5,4]=>[1,2,3,8,5,4,6,7]=>[1,2,3,5,8,4,6,7]
[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[1,2,3,5,8,7,6,4]=>[1,2,3,8,7,6,4,5]=>[1,2,3,6,4,7,8,5]
[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[1,2,3,5,7,8,6,4]=>[1,2,3,8,6,4,5,7]=>[1,2,3,6,4,8,5,7]
[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[1,2,3,6,5,8,7,4]=>[1,2,3,8,7,4,6,5]=>[1,2,3,7,6,4,8,5]
[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[1,2,3,5,6,8,7,4]=>[1,2,3,8,7,4,5,6]=>[1,2,3,7,4,5,8,6]
[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[1,2,3,7,6,5,8,4]=>[1,2,3,8,4,7,6,5]=>[1,2,3,8,6,7,4,5]
[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[1,2,3,6,7,5,8,4]=>[1,2,3,8,4,7,5,6]=>[1,2,3,8,7,5,4,6]
[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[1,2,3,5,7,6,8,4]=>[1,2,3,8,4,5,7,6]=>[1,2,3,8,4,7,5,6]
[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[1,2,3,6,5,7,8,4]=>[1,2,3,8,4,6,5,7]=>[1,2,3,8,6,4,5,7]
[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]
[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[2,3,4,1,6,7,8,5]
[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[4,3,2,1,7,8,6,5]=>[4,3,2,1,8,6,5,7]=>[2,3,4,1,6,8,5,7]
[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]=>[4,3,2,1,6,8,7,5]=>[4,3,2,1,8,7,5,6]=>[2,3,4,1,7,5,8,6]
[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[4,3,2,1,7,6,8,5]=>[4,3,2,1,8,5,7,6]=>[2,3,4,1,8,7,5,6]
[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[4,3,2,1,6,7,8,5]=>[4,3,2,1,8,5,6,7]=>[2,3,4,1,8,5,6,7]
[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[3,4,2,1,8,7,6,5]=>[4,2,1,3,8,7,6,5]=>[2,4,1,3,6,7,8,5]
[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[3,4,2,1,7,8,6,5]=>[4,2,1,3,8,6,5,7]=>[2,4,1,3,6,8,5,7]
[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[3,4,2,1,6,8,7,5]=>[4,2,1,3,8,7,5,6]=>[2,4,1,3,7,5,8,6]
[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]=>[3,4,2,1,7,6,8,5]=>[4,2,1,3,8,5,7,6]=>[2,4,1,3,8,7,5,6]
[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[3,4,2,1,6,7,8,5]=>[4,2,1,3,8,5,6,7]=>[2,4,1,3,8,5,6,7]
[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[2,4,3,1,8,7,6,5]=>[4,3,1,2,8,7,6,5]=>[3,1,4,2,6,7,8,5]
[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[2,4,3,1,7,8,6,5]=>[4,3,1,2,8,6,5,7]=>[3,1,4,2,6,8,5,7]
[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[2,4,3,1,6,8,7,5]=>[4,3,1,2,8,7,5,6]=>[3,1,4,2,7,5,8,6]
[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[2,4,3,1,7,6,8,5]=>[4,3,1,2,8,5,7,6]=>[3,1,4,2,8,7,5,6]
[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[2,4,3,1,6,7,8,5]=>[4,3,1,2,8,5,6,7]=>[3,1,4,2,8,5,6,7]
[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[3,2,4,1,8,7,6,5]=>[4,1,3,2,8,7,6,5]=>[4,3,1,2,6,7,8,5]
[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]=>[3,2,4,1,7,8,6,5]=>[4,1,3,2,8,6,5,7]=>[4,3,1,2,6,8,5,7]
[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]=>[3,2,4,1,6,8,7,5]=>[4,1,3,2,8,7,5,6]=>[4,3,1,2,7,5,8,6]
[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[3,2,4,1,7,6,8,5]=>[4,1,3,2,8,5,7,6]=>[4,3,1,2,8,7,5,6]
[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[3,2,4,1,6,7,8,5]=>[4,1,3,2,8,5,6,7]=>[4,3,1,2,8,5,6,7]
[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[2,3,4,1,8,7,6,5]=>[4,1,2,3,8,7,6,5]=>[4,1,2,3,6,7,8,5]
[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[2,3,4,1,7,8,6,5]=>[4,1,2,3,8,6,5,7]=>[4,1,2,3,6,8,5,7]
[[.,[[[.,.],.],.]],[[.,.],[.,.]]]=>[2,3,4,1,6,8,7,5]=>[4,1,2,3,8,7,5,6]=>[4,1,2,3,7,5,8,6]
[[.,[[[.,.],.],.]],[[.,[.,.]],.]]=>[2,3,4,1,7,6,8,5]=>[4,1,2,3,8,5,7,6]=>[4,1,2,3,8,7,5,6]
[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>[4,1,2,3,8,5,6,7]
[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]=>[1,4,3,2,8,7,6,5]=>[1,3,4,2,6,7,8,5]
[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]=>[1,4,3,2,7,6,8,5]=>[1,4,3,2,8,5,7,6]=>[1,3,4,2,8,7,5,6]
[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[1,4,3,2,6,7,8,5]=>[1,4,3,2,8,5,6,7]=>[1,3,4,2,8,5,6,7]
[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[1,3,4,2,8,7,6,5]=>[1,4,2,3,8,7,6,5]=>[1,4,2,3,6,7,8,5]
[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[1,3,4,2,7,6,8,5]=>[1,4,2,3,8,5,7,6]=>[1,4,2,3,8,7,5,6]
[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[1,3,4,2,6,7,8,5]=>[1,4,2,3,8,5,6,7]=>[1,4,2,3,8,5,6,7]
[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,6,7,8,5]
[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,8,6,5,7]=>[2,1,4,3,6,8,5,7]
[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,8,7,5,6]=>[2,1,4,3,7,5,8,6]
[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,5,7,6]=>[2,1,4,3,8,7,5,6]
[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,5,6,7]=>[2,1,4,3,8,5,6,7]
[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,6,7,8,5]
[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[1,2,4,3,7,6,8,5]=>[1,2,4,3,8,5,7,6]=>[1,2,4,3,8,7,5,6]
[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,5,6,7]
[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]=>[3,2,1,4,8,7,6,5]=>[2,3,1,4,6,7,8,5]
[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]=>[3,2,1,4,7,8,6,5]=>[3,2,1,4,8,6,5,7]=>[2,3,1,4,6,8,5,7]
[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[3,2,1,4,7,6,8,5]=>[3,2,1,4,8,5,7,6]=>[2,3,1,4,8,7,5,6]
[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[3,2,1,4,6,7,8,5]=>[3,2,1,4,8,5,6,7]=>[2,3,1,4,8,5,6,7]
[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[2,3,1,4,8,7,6,5]=>[3,1,2,4,8,7,6,5]=>[3,1,2,4,6,7,8,5]
[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[2,3,1,4,7,6,8,5]=>[3,1,2,4,8,5,7,6]=>[3,1,2,4,8,7,5,6]
[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[2,3,1,4,6,7,8,5]=>[3,1,2,4,8,5,6,7]=>[3,1,2,4,8,5,6,7]
[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,6,7,8,5]
[[[[.,.],[.,.]],.],[[.,[.,.]],.]]=>[1,3,2,4,7,6,8,5]=>[1,3,2,4,8,5,7,6]=>[1,3,2,4,8,7,5,6]
[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,5,6,7]
[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,6,7,8,5]
[[[[.,[.,.]],.],.],[.,[[.,.],.]]]=>[2,1,3,4,7,8,6,5]=>[2,1,3,4,8,6,5,7]=>[2,1,3,4,6,8,5,7]
[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[2,1,3,4,7,6,8,5]=>[2,1,3,4,8,5,7,6]=>[2,1,3,4,8,7,5,6]
[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,5,6,7]=>[2,1,3,4,8,5,6,7]
[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]
[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[1,2,3,4,7,8,6,5]=>[1,2,3,4,8,6,5,7]=>[1,2,3,4,6,8,5,7]
[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,7,6,8,5]=>[1,2,3,4,8,5,7,6]=>[1,2,3,4,8,7,5,6]
[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,5,6,7]
[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[2,3,4,5,1,7,8,6]
[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[5,4,3,2,1,7,8,6]=>[5,4,3,2,1,8,6,7]=>[2,3,4,5,1,8,6,7]
[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[4,5,3,2,1,8,7,6]=>[5,3,2,1,4,8,7,6]=>[2,3,5,1,4,7,8,6]
[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[3,5,4,2,1,8,7,6]=>[5,4,2,1,3,8,7,6]=>[2,4,1,5,3,7,8,6]
[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[4,3,5,2,1,8,7,6]=>[5,2,1,4,3,8,7,6]=>[2,5,4,1,3,7,8,6]
[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]=>[3,4,5,2,1,8,7,6]=>[5,2,1,3,4,8,7,6]=>[2,5,1,3,4,7,8,6]
[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]=>[2,5,4,3,1,8,7,6]=>[5,4,3,1,2,8,7,6]=>[3,1,4,5,2,7,8,6]
[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]=>[2,4,5,3,1,8,7,6]=>[5,3,1,2,4,8,7,6]=>[3,1,5,2,4,7,8,6]
[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[3,2,5,4,1,8,7,6]=>[5,4,1,3,2,8,7,6]=>[4,3,1,5,2,7,8,6]
[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]=>[2,3,5,4,1,8,7,6]=>[5,4,1,2,3,8,7,6]=>[4,1,2,5,3,7,8,6]
[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[4,3,2,5,1,8,7,6]=>[5,1,4,3,2,8,7,6]=>[5,3,4,1,2,7,8,6]
[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]=>[3,4,2,5,1,8,7,6]=>[5,1,4,2,3,8,7,6]=>[5,4,2,1,3,7,8,6]
[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]=>[2,4,3,5,1,8,7,6]=>[5,1,2,4,3,8,7,6]=>[5,1,4,2,3,7,8,6]
[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]=>[3,2,4,5,1,8,7,6]=>[5,1,3,2,4,8,7,6]=>[5,3,1,2,4,7,8,6]
[[.,[[[[.,.],.],.],.]],[.,[.,.]]]=>[2,3,4,5,1,8,7,6]=>[5,1,2,3,4,8,7,6]=>[5,1,2,3,4,7,8,6]
[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,5,8,7,6]=>[2,3,4,1,5,7,8,6]
[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[4,3,2,1,5,7,8,6]=>[4,3,2,1,5,8,6,7]=>[2,3,4,1,5,8,6,7]
[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[3,2,4,1,5,7,8,6]=>[4,1,3,2,5,8,6,7]=>[4,3,1,2,5,8,6,7]
[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[2,3,4,1,5,8,7,6]=>[4,1,2,3,5,8,7,6]=>[4,1,2,3,5,7,8,6]
[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[2,3,4,1,5,7,8,6]=>[4,1,2,3,5,8,6,7]=>[4,1,2,3,5,8,6,7]
[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]=>[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]
[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[2,3,1,4,5,7,8,6]=>[3,1,2,4,5,8,6,7]=>[3,1,2,4,5,8,6,7]
[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]
[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,6,7]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[2,3,4,5,6,1,8,7]
[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[5,6,4,3,2,1,8,7]=>[6,4,3,2,1,5,8,7]=>[2,3,4,6,1,5,8,7]
[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[4,5,6,3,2,1,8,7]=>[6,3,2,1,4,5,8,7]=>[2,3,6,1,4,5,8,7]
[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[3,6,5,4,2,1,8,7]=>[6,5,4,2,1,3,8,7]=>[2,4,1,5,6,3,8,7]
[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[4,3,6,5,2,1,8,7]=>[6,5,2,1,4,3,8,7]=>[2,5,4,1,6,3,8,7]
[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[5,4,3,6,2,1,8,7]=>[6,2,1,5,4,3,8,7]=>[2,6,4,5,1,3,8,7]
[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[4,5,3,6,2,1,8,7]=>[6,2,1,5,3,4,8,7]=>[2,6,5,3,1,4,8,7]
[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[4,3,5,6,2,1,8,7]=>[6,2,1,4,3,5,8,7]=>[2,6,4,1,3,5,8,7]
[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[2,3,6,5,4,1,8,7]=>[6,5,4,1,2,3,8,7]=>[4,1,2,5,6,3,8,7]
[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[2,4,3,6,5,1,8,7]=>[6,5,1,2,4,3,8,7]=>[5,1,4,2,6,3,8,7]
[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[5,4,3,2,6,1,8,7]=>[6,1,5,4,3,2,8,7]=>[6,3,4,5,1,2,8,7]
[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[4,3,5,2,6,1,8,7]=>[6,1,5,2,4,3,8,7]=>[6,5,4,2,1,3,8,7]
[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[3,2,5,4,6,1,8,7]=>[6,1,3,2,5,4,8,7]=>[6,3,1,5,2,4,8,7]
[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]=>[4,3,2,5,6,1,8,7]=>[6,1,4,3,2,5,8,7]=>[6,3,4,1,2,5,8,7]
[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>[6,1,2,3,4,5,8,7]
[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]=>[1,5,6,4,3,2,8,7]=>[1,6,4,3,2,5,8,7]=>[1,3,4,6,2,5,8,7]
[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]=>[2,1,6,5,4,3,8,7]=>[2,1,4,5,6,3,8,7]
[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[2,1,5,6,4,3,8,7]=>[2,1,6,4,3,5,8,7]=>[2,1,4,6,3,5,8,7]
[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[2,1,4,6,5,3,8,7]=>[2,1,6,5,3,4,8,7]=>[2,1,5,3,6,4,8,7]
[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[2,1,5,4,6,3,8,7]=>[2,1,6,3,5,4,8,7]=>[2,1,6,5,3,4,8,7]
[[[.,[.,.]],[[[.,.],.],.]],[.,.]]=>[2,1,4,5,6,3,8,7]=>[2,1,6,3,4,5,8,7]=>[2,1,6,3,4,5,8,7]
[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[2,3,4,1,6,5,8,7]
[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[3,4,2,1,6,5,8,7]=>[4,2,1,3,6,5,8,7]=>[2,4,1,3,6,5,8,7]
[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[2,4,3,1,6,5,8,7]=>[4,3,1,2,6,5,8,7]=>[3,1,4,2,6,5,8,7]
[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[3,2,4,1,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>[4,3,1,2,6,5,8,7]
[[[.,[[[.,.],.],.]],[.,.]],[.,.]]=>[2,3,4,1,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>[4,1,2,3,6,5,8,7]
[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]
[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[2,3,4,5,1,6,8,7]
[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[2,1,4,5,3,6,8,7]
[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[2,3,4,1,5,6,8,7]
[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[3,2,4,1,5,6,8,7]=>[4,1,3,2,5,6,8,7]=>[4,3,1,2,5,6,8,7]
[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[2,3,4,1,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>[4,1,2,3,5,6,8,7]
[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]
[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]
[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,1,8]
[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[7,5,4,3,2,1,6,8]=>[2,3,4,5,7,1,6,8]
[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[5,7,6,4,3,2,1,8]=>[7,6,4,3,2,1,5,8]=>[2,3,4,6,1,7,5,8]
[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[7,4,3,2,1,6,5,8]=>[2,3,4,7,6,1,5,8]
[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[7,4,3,2,1,5,6,8]=>[2,3,4,7,1,5,6,8]
[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[4,7,6,5,3,2,1,8]=>[7,6,5,3,2,1,4,8]=>[2,3,5,1,6,7,4,8]
[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[7,3,2,1,6,5,4,8]=>[2,3,7,5,6,1,4,8]
[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[7,3,2,1,4,5,6,8]=>[2,3,7,1,4,5,6,8]
[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[3,4,7,6,5,2,1,8]=>[7,6,5,2,1,3,4,8]=>[2,5,1,3,6,7,4,8]
[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[3,2,7,6,5,4,1,8]=>[7,6,5,4,1,3,2,8]=>[4,3,1,5,6,7,2,8]
[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[3,2,6,7,5,4,1,8]=>[7,5,4,1,3,2,6,8]=>[4,3,1,5,7,2,6,8]
[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[5,4,3,2,7,6,1,8]=>[7,6,1,5,4,3,2,8]=>[6,3,4,5,1,7,2,8]
[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[3,2,5,4,7,6,1,8]=>[7,6,1,3,2,5,4,8]=>[6,3,1,5,2,7,4,8]
[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[2,3,4,5,7,6,1,8]=>[7,6,1,2,3,4,5,8]=>[6,1,2,3,4,7,5,8]
[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[7,1,6,2,5,3,4,8]=>[7,6,5,3,2,1,4,8]
[[.,[[[.,[[.,.],[.,.]]],.],.]],.]=>[3,5,4,2,6,7,1,8]=>[7,1,5,4,2,3,6,8]=>[7,4,2,5,1,3,6,8]
[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[3,2,4,5,6,7,1,8]=>[7,1,3,2,4,5,6,8]=>[7,3,1,2,4,5,6,8]
[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]
[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[1,3,4,6,7,5,2,8]=>[1,7,5,2,3,4,6,8]=>[1,5,2,3,7,4,6,8]
[[[.,.],[[[[.,.],.],.],[.,.]]],.]=>[1,3,4,5,7,6,2,8]=>[1,7,6,2,3,4,5,8]=>[1,6,2,3,4,7,5,8]
[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[2,3,1,5,6,7,4,8]=>[3,1,2,7,4,5,6,8]=>[3,1,2,7,4,5,6,8]
[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,7,6,5,8]=>[2,3,4,1,6,7,5,8]
[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]=>[4,3,2,1,6,7,5,8]=>[4,3,2,1,7,5,6,8]=>[2,3,4,1,7,5,6,8]
[[[.,[[[.,.],.],.]],[.,[.,.]]],.]=>[2,3,4,1,7,6,5,8]=>[4,1,2,3,7,6,5,8]=>[4,1,2,3,6,7,5,8]
[[[.,[[[.,.],.],.]],[[.,.],.]],.]=>[2,3,4,1,6,7,5,8]=>[4,1,2,3,7,5,6,8]=>[4,1,2,3,7,5,6,8]
[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]=>[1,4,3,2,7,6,5,8]=>[1,3,4,2,6,7,5,8]
[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[1,3,4,2,6,7,5,8]=>[1,4,2,3,7,5,6,8]=>[1,4,2,3,7,5,6,8]
[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]=>[3,2,1,4,7,6,5,8]=>[2,3,1,4,6,7,5,8]
[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[2,3,4,5,1,7,6,8]
[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[2,3,1,5,4,7,6,8]
[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[2,3,1,5,4,7,6,8]=>[3,1,2,5,4,7,6,8]=>[3,1,2,5,4,7,6,8]
[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]
[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]
[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[2,3,4,1,5,7,6,8]
[[[[.,[[.,[.,.]],.]],.],[.,.]],.]=>[3,2,4,1,5,7,6,8]=>[4,1,3,2,5,7,6,8]=>[4,3,1,2,5,7,6,8]
[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[2,3,4,1,5,7,6,8]=>[4,1,2,3,5,7,6,8]=>[4,1,2,3,5,7,6,8]
[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]
[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]
[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[2,3,4,5,6,1,7,8]
[[[.,[[[[.,.],.],.],[.,.]]],.],.]=>[2,3,4,6,5,1,7,8]=>[6,5,1,2,3,4,7,8]=>[5,1,2,3,6,4,7,8]
[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>[6,1,2,3,4,5,7,8]
[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[1,2,4,6,5,3,7,8]=>[1,2,6,5,3,4,7,8]=>[1,2,5,3,6,4,7,8]
[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[2,3,4,1,6,5,7,8]
[[[[.,[[[.,.],.],.]],[.,.]],.],.]=>[2,3,4,1,6,5,7,8]=>[4,1,2,3,6,5,7,8]=>[4,1,2,3,6,5,7,8]
[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]
[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]
[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[3,2,5,4,1,6,7,8]=>[5,4,1,3,2,6,7,8]=>[4,3,1,5,2,6,7,8]
[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]
[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]
[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]
[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]
[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[4,3,1,2,5,6,7,8]
[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]
[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]
[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]
[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]
[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]
[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,1]
[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[8,9,7,6,5,4,3,2,1]=>[9,7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,9,1,8]
[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]=>[7,8,9,6,5,4,3,2,1]=>[9,6,5,4,3,2,1,7,8]=>[2,3,4,5,6,9,1,7,8]
[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,8]
[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]
[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,10,1]
[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]=>[9,10,8,7,6,5,4,3,2,1]=>[10,8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,10,1,9]
[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]=>[6,7,8,9,10,5,4,3,2,1]=>[10,5,4,3,2,1,6,7,8,9]=>[2,3,4,5,10,1,6,7,8,9]
[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>[1,9,2,3,4,5,6,7,8]
[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>[10,1,2,3,4,5,6,7,8,9]
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]
[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]=>[8,7,9,6,5,4,3,2,1]=>[9,6,5,4,3,2,1,8,7]=>[2,3,4,5,6,9,8,1,7]
[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]=>[8,7,6,9,5,4,3,2,1]=>[9,5,4,3,2,1,8,7,6]=>[2,3,4,5,9,7,8,1,6]
[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]=>[8,7,6,5,9,4,3,2,1]=>[9,4,3,2,1,8,7,6,5]=>[2,3,4,9,6,7,8,1,5]
[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]=>[8,7,6,5,4,9,3,2,1]=>[9,3,2,1,8,7,6,5,4]=>[2,3,9,5,6,7,8,1,4]
[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]=>[8,7,6,5,4,3,9,2,1]=>[9,2,1,8,7,6,5,4,3]=>[2,9,4,5,6,7,8,1,3]
[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]=>[8,7,6,5,4,3,2,9,1]=>[9,1,8,7,6,5,4,3,2]=>[9,3,4,5,6,7,8,1,2]
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,1,9]
[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]=>[9,8,10,7,6,5,4,3,2,1]=>[10,7,6,5,4,3,2,1,9,8]=>[2,3,4,5,6,7,10,9,1,8]
[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]=>[9,8,7,10,6,5,4,3,2,1]=>[10,6,5,4,3,2,1,9,8,7]=>[2,3,4,5,6,10,8,9,1,7]
[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]=>[9,8,7,6,10,5,4,3,2,1]=>[10,5,4,3,2,1,9,8,7,6]=>[2,3,4,5,10,7,8,9,1,6]
[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]=>[9,8,7,6,5,10,4,3,2,1]=>[10,4,3,2,1,9,8,7,6,5]=>[2,3,4,10,6,7,8,9,1,5]
[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]=>[9,8,7,6,5,4,10,3,2,1]=>[10,3,2,1,9,8,7,6,5,4]=>[2,3,10,5,6,7,8,9,1,4]
[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]=>[9,8,7,6,5,4,3,10,2,1]=>[10,2,1,9,8,7,6,5,4,3]=>[2,10,4,5,6,7,8,9,1,3]
[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]=>[9,8,7,6,5,4,3,2,10,1]=>[10,1,9,8,7,6,5,4,3,2]=>[10,3,4,5,6,7,8,9,1,2]
[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,8,9,1,10]
[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]
[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]
[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]
[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>[9,1,3,2,4,5,6,7,8]=>[9,3,1,2,4,5,6,7,8]
[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]
[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>[9,1,4,2,3,5,6,7,8]=>[9,4,2,1,3,5,6,7,8]
[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,1,2,3,4,5,6,7,8,9,10]=>[11,1,2,3,4,5,6,7,8,9,10]
[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,9,7,8]
[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,9,6,7,8]=>[1,2,3,4,5,9,6,7,8]
[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,4,6,7,8,9,5]=>[1,2,3,4,9,5,6,7,8]=>[1,2,3,4,9,5,6,7,8]
[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]=>[1,2,3,5,6,7,8,9,4]=>[1,2,3,9,4,5,6,7,8]=>[1,2,3,9,4,5,6,7,8]
[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,3]=>[1,2,9,3,4,5,6,7,8]=>[1,2,9,3,4,5,6,7,8]
[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,8,9,7]
[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,10,8,9]=>[1,2,3,4,5,6,7,10,8,9]
[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]=>[1,2,3,4,5,8,7,9,6]=>[1,2,3,4,5,9,6,8,7]=>[1,2,3,4,5,9,8,6,7]
[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,10,7,8,9]=>[1,2,3,4,5,6,10,7,8,9]
[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,10,6,7,8,9]=>[1,2,3,4,5,10,6,7,8,9]
[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,10,5,6,7,8,9]=>[1,2,3,4,10,5,6,7,8,9]
[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,10,4,5,6,7,8,9]=>[1,2,3,10,4,5,6,7,8,9]
[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]=>[1,2,4,5,6,7,8,9,10,3]=>[1,2,10,3,4,5,6,7,8,9]=>[1,2,10,3,4,5,6,7,8,9]
[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>[1,10,2,3,4,5,6,7,8,9]
[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]=>[1,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,2]
[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>[8,6,5,4,3,2,1,7,9]=>[2,3,4,5,6,8,1,7,9]
[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[1,8,9,7,6,5,4,3,2]=>[1,9,7,6,5,4,3,2,8]=>[1,3,4,5,6,7,9,2,8]
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,2]
[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[2,3,4,5,6,7,8,9,10,1,11]
[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>[9,7,6,5,4,3,2,1,8,10]=>[2,3,4,5,6,7,9,1,8,10]
[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[1,8,7,9,6,5,4,3,2]=>[1,9,6,5,4,3,2,8,7]=>[1,3,4,5,6,9,8,2,7]
[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]=>[1,9,10,8,7,6,5,4,3,2]=>[1,10,8,7,6,5,4,3,2,9]=>[1,3,4,5,6,7,8,10,2,9]
[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,11,2]
[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,9,10,3]
[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]=>[4,3,2,1,10,9,8,7,6,5]=>[2,3,4,1,6,7,8,9,10,5]
[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[6,5,4,3,2,1,10,9,8,7]=>[6,5,4,3,2,1,10,9,8,7]=>[2,3,4,5,6,1,8,9,10,7]
[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[8,7,6,5,4,3,2,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[2,3,4,5,6,7,8,1,10,9]
[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>[2,3,4,5,6,7,1,8,9]
[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>[2,3,4,5,6,1,7,8,9]
[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]
[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[2,3,4,1,5,6,7,8,9]
[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]
[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]
[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>[2,3,4,5,6,7,8,1,9,10]
[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]
[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]
[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]
[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]
[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]
[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]
[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]
[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>[8,1,2,3,4,5,6,7,9]
[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>[7,1,2,3,4,5,6,8,9]
[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>[9,1,2,3,4,5,6,7,8,10]
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
Map
invert Laguerre heap
Description
The permutation obtained by inverting the corresponding Laguerre heap, according to Viennot.
Let $\pi$ be a permutation. Following Viennot [1], we associate to $\pi$ a heap of pieces, by considering each decreasing run $(\pi_i, \pi_{i+1}, \dots, \pi_j)$ of $\pi$ as one piece, beginning with the left most run. Two pieces commute if and only if the minimal element of one piece is larger than the maximal element of the other piece.
This map yields the permutation corresponding to the heap obtained by reversing the reading direction of the heap.
Equivalently, this is the permutation obtained by flipping the noncrossing arc diagram of Reading [2] vertically.
By definition, this map preserves the set of decreasing runs.
Let $\pi$ be a permutation. Following Viennot [1], we associate to $\pi$ a heap of pieces, by considering each decreasing run $(\pi_i, \pi_{i+1}, \dots, \pi_j)$ of $\pi$ as one piece, beginning with the left most run. Two pieces commute if and only if the minimal element of one piece is larger than the maximal element of the other piece.
This map yields the permutation corresponding to the heap obtained by reversing the reading direction of the heap.
Equivalently, this is the permutation obtained by flipping the noncrossing arc diagram of Reading [2] vertically.
By definition, this map preserves the set of decreasing runs.
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
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